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</div><h2>SL Paper 2</h2><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">Tomek is attending a conference in Singapore. He has both trousers and shorts to wear. He also has the choice of wearing a tie or not.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The probability Tomek wears trousers is \(0.3\). If he wears trousers, the probability that he wears a tie is \(0.8\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">If Tomek wears shorts, the probability that he wears a tie is \(0.15\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">The following tree diagram shows the probabilities for Tomek’s clothing options at the conference.</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><img src="images/Schermafbeelding_2014-09-02_om_11.36.02.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of</span></p>
<p><span>(i) \({\text{A}}\);</span></p>
<p><span>(ii) \({\text{B}}\);</span></p>
<p><span>(iii) \({\text{C}}\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the probability that Tomek wears</span></p>
<p><span>(i) shorts and no tie;</span></p>
<p><span>(ii) no tie;</span></p>
<p><span>(iii) shorts given that he is not wearing a tie.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The conference lasts for two days.</span></p>
<p><span>Calculate the probability that Tomek wears trousers on both days.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The conference lasts for two days.</span></p>
<p><span>Calculate the probability that Tomek wears trousers on one of the days, and shorts on the other day.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(0.7 \left( {\frac{{70}}{{100}},{\text{ }}\frac{7}{{10}},{\text{ 70% }}} \right)\) <strong><em>(A1)</em></strong></span></p>
<p><span>(ii) \(0.2 \left( {\frac{{20}}{{100}},{\text{ }}\frac{2}{{10}},{\text{ }}\frac{1}{5},{\text{ 20% }}} \right)\) <strong><em>(A1)</em></strong></span></p>
<p><span>(iii) \(0.85 \left( {\frac{{85}}{{100}},{\text{ }}\frac{{17}}{{20}},{\text{ 85% }}} \right)\) <strong><em>(A1)</em></strong></span></p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(0.7 \times 0.85\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying their values from parts (a)(i) and (a)(iii).</span></p>
<p> </p>
<p><span>\( = 0.595{\text{ }}\left( {\frac{{119}}{{200}},{\text{ 59.5% }}} \right)\) <strong><em>(A1)</em>(ft)<em>(G1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (a).</span></p>
<p> </p>
<p><span>(ii) \(0.3 \times 0.2 + 0.7 \times 0.85\) <strong><em>(M1)(M1)</em></strong></span></p>
<p><span><strong><em> </em></strong></span></p>
<p><span><strong>Note: </strong>A</span><span>ward <strong><em>(M1) </em></strong>for their two products, <strong><em>(M1) </em></strong>for adding their two products.</span></p>
<p> </p>
<p><span>\( = 0.655{\text{ }}\left( {\frac{{131}}{{200}},{\text{ 65.5% }}} \right)\) <strong><em>(A1)</em>(ft)(<em>G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (a)<span>.</span></span></p>
<p> </p>
<p><span>(iii) \(\frac{{0.595}}{{0.655}}\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></span></p>
<p> </p>
<p><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft) </strong>for correct numerator, <strong><em>(A1)</em>(ft) </strong>for correct denominator. Follow through from parts (b)(i) and (ii).</span></p>
<p> </p>
<p><span>\( = 0.908{\text{ }}\left( {{\text{0.90839}} \ldots ,{\text{ }}\frac{{119}}{{131}},{\text{ 90,8% }}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[8 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.3\) <strong><em>(M1)</em></strong></span></p>
<p><span>\( = 0.09 \left( {\frac{9}{{100}}, 9\%} \right)\) <strong><em>(A1)(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.7\) <strong><em>(M1)</em></strong></span></p>
<p><span>\(0.3 \times 0.7 \times 2\) <strong>OR</strong> \((0.3 \times 0.7) + (0.7 \times 0.3)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product seen, <strong><em>(M1) </em></strong>for multiplying their product by 2 or for adding their products twice.</span></p>
<p> </p>
<p><span>\( = 0.42 \left( {\frac{{42}}{{100}}, \frac{{21}}{{50}}, 42\%} \right)\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Note: </strong></span><span>Follow through from part (a)(i)<span>.</span></span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>A company performs an experiment on the efficiency of a liquid that is used to detect a nut allergy.</p>
<p>A group of 60 people took part in the experiment. In this group 26 are allergic to nuts. One person from the group is chosen at random.</p>
</div>
<div class="specification">
<p>A second person is chosen from the group.</p>
</div>
<div class="specification">
<p>When the liquid is added to a person’s blood sample, it is expected to turn blue if the person is allergic to nuts and to turn red if the person is not allergic to nuts.</p>
<p>The company claims that the probability that the test result is correct is 98% for people who are allergic to nuts and 95% for people who are not allergic to nuts.</p>
<p>It is known that 6 in every 1000 adults are allergic to nuts.</p>
<p>This information can be represented in a tree diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-13_om_14.31.34.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c.d.e.f.g"></p>
</div>
<div class="specification">
<p>An adult, who was not part of the original group of 60, is chosen at random and tested using this liquid.</p>
</div>
<div class="specification">
<p>The liquid is used in an office to identify employees who might be allergic to nuts. The liquid turned blue for <strong>38 </strong><strong>employees</strong>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this person is <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that both people chosen are <strong>not </strong>allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>and complete the tree diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that this adult is allergic to nuts and the liquid turns blue.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the liquid turns blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that the tested adult is allergic to nuts given that the liquid turned blue.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the number of employees, from this 38, who are allergic to nuts.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{34}}{{60}}{\text{ }}\left( {\frac{{17}}{{30}},{\text{ }}0.567,{\text{ }}0.566666 \ldots ,{\text{ }}56.7\% } \right)\) <strong><em>(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{34}}{{60}} \times \frac{{33}}{{59}}\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct product.</p>
<p> </p>
<p>\( = 0.317{\text{ }}\left( {\frac{{187}}{{590}},{\text{ }}0.316949 \ldots ,{\text{ }}31.7\% } \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from part (a).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2018-02-14_om_05.54.09.png" alt="N17/5/MATSD/SP2/ENG/TZ0/04.c/M"> <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for each correct pair of branches.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.006 \times 0.98\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 0.006 by 0.98.</p>
<p> </p>
<p>\( = 0.00588{\text{ }}\left( {\frac{{147}}{{25000}},{\text{ }}0.588\% } \right)\) <strong><em>(A1)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.006 \times 0.98 + 0.994 \times 0.05{\text{ }}(0.00588 + 0.994 \times 0.05)\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their two correct products, <strong><em>(M1) </em></strong>for adding two products.</p>
<p> </p>
<p>\( = 0.0556{\text{ }}\left( {0.05558,{\text{ }}5.56\% ,{\text{ }}\frac{{2779}}{{50000}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (c) and (d).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{0.006 \times 0.98}}{{0.05558}}\) <strong><em>(M1)(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for their correct numerator, <strong><em>(M1) </em></strong>for their correct denominator.</p>
<p> </p>
<p>\( = 0.106{\text{ }}\left( {0.105793 \ldots ,{\text{ }}10.6\% ,{\text{ }}\frac{{42}}{{397}}} \right)\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Follow through from parts (d) and (e).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(0.105793 \ldots \times 38\) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for multiplying 38 by their answer to part (f).</p>
<p> </p>
<p>\( = 4.02{\text{ }}(4.02015 \ldots )\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Notes: </strong>Follow through from part (f). Use of 3 sf result from part (f) results in an answer of 4.03 (4.028).</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Beartown has three local newspapers: <em>The Art Journal</em>, <em>The Beartown News</em>, and <em>The Currier</em>.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A survey shows that</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">32 % of the town’s population read <em>The Art Journal</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">46 % read <em>The Beartown News</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">54 % read <em>The Currier</em>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">3 % read <em>The Art Journal</em> and <em>The Beartown News</em> <strong>only</strong>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">8 % read <em>The Art Journal</em> and <em>The Currier</em> <strong>only</strong>,</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">12 % read <em>The Beartown News</em> and <em>The Currier</em> <strong>only</strong>, and</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">5 % of the population reads <strong>all</strong> three newspapers.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to represent this information. Label<em> A</em> the set that represents <em>The Art Journal</em> readers, <em>B</em> the set that represents <em>The Beartown News</em> readers, and <em>C</em> the set that represents <em>The Currier</em> readers.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of the population that does not read any of the three newspapers.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of the population that reads exactly one newspaper.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of the population that reads <em>The Art Journal</em> or <em>The Beartown News</em> but not <em>The Currier</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A local radio station states that 83 % of the population reads either <em>The Beartown News</em> or <em>The Currier</em>.</span></p>
<p><span>Use your Venn diagram to decide whether the statement is true. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The population of Beartown is 120 000. The local radio station claimed that 34 000 of the town’s citizens read at least two of the local newspapers.</span></p>
<p><span>Find the percentage error in this claim.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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Ct9jQS57jJ8NVztFiEIfmt+aE5WqxUhpNJlwIKVcnUBy9FIRiMXofofijwRV9152MiTcgxZuNZiEUI1x+1jWVbVhfnIPwHGGKUUye4ELkI1P7HSWf50qnbgMGdoGLJwrcUi5DgO2noExlg9+/LwzPKJQDiIwSXkIlTzEzGH6TWYZQ2JkBOhlCL5glosQrIso9154DhOPXtl8Nu6pmkYXEIuQnU+DrlZ1pClqO0phQmCAMl31FYR8jwP7WoQY0xRlNoE0jAMDLN8Gki+KS5CdT4Oc4AOecIashR40gBpGIaBYWWorSKEeeat2fiQzPIZjEajxktCuQjV+bjRaIRkvWGfOtP4SNIAacDu2sZlspUihDzYn06nNbuBo9EI7QowY8yyrMYdLi5CtT2rtlx0MepM4+N3EOvM2aTRShHCHOwzxmRZrlkSkGef4dL7ZtvARai2Z2GY19KoP0WG3EGcTqeNlye0UoQwB/tQ+1jzQyGsrvmhR9F4Ro6LUD0PQpLhSaP+Obf+vMhRYFi4ap8IzWazxt3qDJqyOeQOV+MZOS5C9TzIMAzMc279JbWNeKVH0XiZcftESNO0Iy8yqJX6c3FA47N8No0nx7kI1fAUKDxDu1jblNff1JyQk8Yzcu0ToSOtfO3Z1FSHRKJ+8m//ocP91sl/cBwNxrae52FeDWZ17d5Ng4tQDU9Bvn+8qdmWZ+SyaZkIHbnEDbfmkGSNuT9Deqia/yzrAGnHcRr0KRrP7WZjGEaDISwXoRqegrkkgTGmaVojzcO/ZNtsrNYyESriU4RzcyjsihDcpiNcmPN1ic1rysoBRVEwR/2z2azBWI2LUD1PQZuLgwMCmvLSmk0DHKTZWK1lIlRoln9HpbPHInS7pC8Ecn5B35ZziduWZgchpRTzshDMAk09nYtQ1Y9ofNkvm2Z3LyFfyW42VmuZCBVa9twTIYiNBOmrrySBEELOpYnjlyFHFX0Coe9MYOGKnEv6D17K/aee52HOyLOCX185cBGq+hHId+81mw1ufPH/IA1uomiZCBV6xK4IhZ45jO4SDf2biSQQYWjOT5ShqmoxNzcT9a83/u32ptTUpsICY/kNKA9FUZra4IX8k6maGrqPfEGoKtu7n0AIIUSQJtdecnof/7JQgyLdRxG6c/WzR7dc3+iiQIamd5oK1RKIvKPSmaDaaQtZyGsTuAg1RT0ihHYLOasqCv/gTq4mN37IWOhfjzOnEeRjk1La1DF3bRKhoosKh0QI/uBMd+9Oal4dIrS21bMXdJlay4d8ImiwcIOLUA2PwDzJVv8J3Pn0kghje52sQsjHJhehXBSd5ffWhNa2KpBYPHEgvMjJbDarUoTCjfeDLg1j2plAs+V5B0Fl6L0Ca5aiPqpv3ntbHWbUOiEfmw0WyPVAhKAM4VGYDNVxw7G9DGGhpYxa7Spn2I2ri+SerKK+Bmf5PHARaoqei1DlZ+dsvGtdOst0ZJGPzQbLmjouQneufkYiRN3dbH+z9uj4fl4X1VduCcVxlRtZ6LtUlwSSEfIjN/QGi8gxT5E1UHX3kS+8VzrDxicZ4YIuU6aSZneyH4SLUC6Qn35RiwB89MznhFxSP3n9Cvm5KRVnLLPgIlTp+yPfHlB98259l+rSOXm02FxzG06Ci1AukLv5tdQ4hmt7LIgTt51bhVAZeq/ouQjV4/2EnjkkZxJ9l/hb5B9Rg3vJuQiVRg3VL6F/PRafje20iB+7oXMRaoqei1BNU8faVoVnuvsh8ZfNnhiSBy5Ch0EuQpZlVdC8cONOtjUJgqh+8zpz+Qr5XMBFqClqGJuYj4yqY+oIl/b4mTi+zhifyI2Qi9BhkIsQhuYhF6EG12aRj/+q4WOzkubBPvdtfZOZ7SGiN0IuQofpqaEfA3IR4iXaTcHHJoZADbkRchE6DPLqOAzNQ14GykWoKXqejkPinGE2wgavIW+TCCGxpDQwNA+5Q1rNslkuMI//Gqi6+w0W3+cBw9hEXpiAar2Wi1BBMDQPuQjxA0ybgo/NBi8TitqA/CPiInQYDJaUAYbmIb9clYtQU/RchBgCA0D+EXERQvSIU2i8ebIsYz6pl4tQU1Td/QZXFHLSuAHgX6/Fc6QWF6HiVNG81WrleR7NwXQ6xX+cflPNQ245VcPHZuPNQ54qR1U0xEWoOIPB4PQrcoMgmM1mlmUpikIIGQwGiqIYhnFQhFRV/fTTT6OXUEpRRUXNXvyK3HKqho/NBq+vBpCnyrkI5aVxS8rGMIzCIe1qtbIsS5ZlQkgkIUfFDVGF0mq1AhmL3m06nTYeIU2n0wbTEcinyKqpofvVXF1aGuWmgheLxWw2o5RqmgajLBtZlp88eWIYhuM4qFzDCFQXTqIWoQYvQs/DbDYrUJswm800TSOEGIZxioEmFkBDXKUoymAwMAyjwWlCluUGL/XiIlT1I5DfHHqKgwgsFgtwpAaDwWg0Ak8RROWgh+d5HiEERGs0GsUdzVOaVCKlZHGK0TIRQr64x47xB4MgcBxnNBqNRqNSIpXsqgSItCBTV39aAHJxDUZjXISqfgTym0Nns9loNCrwwiAIKKUwTiGUKeDJLRaL+NNXq5XjOIZhjEajwWBgWVazQaTnecU+nFJomQjhL8LJE6utVitKabl6kHMrXFz5HMepTRWazcUxLkLVdx/DiSHZHOvse55nGAYhRNO0E0OWjA9nsVhET2lq0ciyrAYPvGiZCDH0y0LZGbkgCCzLgsxbub04dst6lKOrx3tt3E3mIlT1I3acfYTkT+Y7jiPL8mg0opSWEqMctP8gCKbTaeQdnv7Eo2h2Um2fCJ2e262atIwcxLyKolQRekP53LGv8jxvMBhomlZpSARRWrOVEVyEangK8tqEPEu28TxBiY/O/8nA5ciDwYBSWs+Qadx7aJ8INZu+zIOmaTsOVxAEsJ5ZnY9TeF0R2jYajapbIwW/sqI3zwkXoRqe0ni8e5AMMYh8xNJzYgVmeTi/oNJRGdFsLo61UYQYY6PRCHPF/c6cO5vN8kcb4ZJebC8oIeS56X3M88TTfRnHcWCB9JQ3SQNDTSMXoRqegsHbyGbfQWTbJPlgMKjISi3LKrZaNp1OqxuVEY1Pp60UIeRLoFH2KTLu3N/xB1f/XNRvNkc+sRRfZrVaybIsy3Lp2WEMWRouQjU8JQgCDN91BvvltZGPWF2zZVkuPMtXNyqj92+81KuVItR4ve9BDMP45ptvZFk+agUoXNKLsxd0eXvs40r0ZSilhJASkyqQ4y7r3QrDRaieByFfso0vTx7tI4Zv6cX5NkshDM155jWq95Qyy8OorCJQw+DQt1KEGGOapmE+iOmnn3762c9+9ve///2YF7231aeEECJI+nc/eps8Fs7YtrigQCPTWCwWJS5fNVLtsw8XoXoehH/JFjZNQwb7GB8x3LgTUZy4uQcmUNbmhKjB5TrfzW4hB9oqQjDz4gyGYBL/4osviny7oe++/kYVBSJcmPN1nlfA1uujH5RJWTpUeIdg6XARqu1Zja8xZOM4zm9/+9ujA4vwLb0QL+jb4ySIMUVRyprlgyAwDKPEow2QeAxtFSFW6rdbItH0fdL8u3ljSuckh9sFwX4VYlyKDuH5jrgI1fYsJAnYNBzH+eSTT3744YdjXhSu7bFACCHnkv4P28vlHbJqfGWoISpFh6rwXwvQYhHC42VH7EzcsiwX/o5DzxwSUXcP1CgYhlFdSvdEHYIvCEm0ykWotmdBeQKeU9HiwAz+/fffF5LJW9/9p6kOCTmXzDd5qoeK7d47SCk6BKMbw/BssQix02b50gmCQJbl+Kos+EEFq27WtiocECEwo0qLkQrrEMxEeNIy1RhnNCttEVXztevfh68bVxeTjlQWRPWbh7+qhZrHJpzUWecT8xDN3afJ5HpuXgjkme5+yP67SuunTtchPMvq7RahxWJBCMFwig8o0H5QAtcCFXjD0DOHmem4IAjg5NMCb34UxXTIMAxU01AFxgmTESHimEJ+ZjOn6pAQIkiv5tsvLvTMISGEnEn0HWOMhf7NRBIIITlmsRKpeWzCLI9hYEbMZrP4XAFn5BRUiHBuDoUz3b3L/KtKsxTsNB2CwnQMYRBruwgxxiilGPbHaZqWKDYgFXkCgtB3X9N/uf4tY+HGo6r4efYkVVjeCnCsDiEsGynbOG+X9IWwv6E4nJtDgRAiXNAlyJBPpbgIMYhxCSHk4CxWIvWPTSQDE0g04BNWRN7b6tPsrw9m+aq3TBXTofyTUj20XoQYgqRctlcF5njQUEL/eiwK23SNmb34mdfEN55Nv1HF84cZkDHGbv2br6X7cxmG6qubPIkhGMZ5zL22EO0oSjbOzY0OX9bQ9B59eh898/mj0y5SRSjvRpNSaGRs7mSnmyLNhSqeRwnn5jDLR6wzF11Ah+r0X/PQBRGCCrGmYn8w8ez8MniFZUUGuR2Z7caj+AzIwo37F0ml3ibcpoaEnGc05PRtsZk4UK5xbpNs+9HMnU8vH21m3BGh+8/8XJo4dS4KNTI2YWA2W6Gwv1IbJ2+4Fvrua3q/jLeZU/VZ9pDRNK3OXDToUM7p5aSF6mroggixRmP/nHFYiXZ51CwfeubwkQi9t/VvHpaaIH2UOzF0sLOocs1xyjXOO1c/SxahvV/di1CM4zc8nk5TY/OkpZcyODhYEpdydwmX9nhbfiKqpu1lKBCcw324y8lZChb6zkQ632ZEvnX9XOenGIaRZ05oS5ailSLEGkrK5Rc/+PpPb+HRjoxPpUcitMM7Kp0Jqp1z40O2b4utIi5O7ZHQ9jN/iITebtyJCJPL+LrW2rhGx6aiKE0l5fIMFjDpEveT5gv+ErMUjG1udOmKeuuHnHk+lyWnurQlS9FWEaqhXnn/iUfllEvZ/nm0I5MtQmtbFZ6q9vv870cpTSvByOVUNkTJxrktQDhyTeiDqz8jhBByXmDv/Sk0ODabypbDvJxnuIFWldLCoxIee1mKcG1/PXlYagJbOrxZEDiouC3KUrRVhBhjlmWVuPRykITqmtB3X6kiSV3z9zzvlJrynEH3I7JE6HZJX5xFdVz5SFyRQq5ArLbquPuChdgy286aEJyFQQgRipxUW5hmx2Yj2fKjNgnApQknTh1HF4UeyFLc+fSSCGN7nXd8ZgQ64AG3JUvRYhFijBmGUY+5JyW7YWIaqnS+YeFm/koSEiqgClf3Q9eOHifphh4u6cWwyPoEZL2j/+JXINb8PqEHS3i4Mkp8aefL+J9O42Oz5mx5gU0CBcfXlvyB1wMHROi9rT7Nnypn6clAUCAkW1P36ZoI1TMhpnzZG1cXY55L6nILuF1H6VDxEZJm6Js3pqoXngSj8dYKBWJVGWe48X78TpeiawgFSf/uYdV678SE+xWkKIoi+ZMtJ9L42Cz3aPZsUhZIbn33W/VhF0TCmn/abr88TywyCjJFqNjFLtPpdMcLh08e8wjtmgixWqbFlHURmFy26f5wbg5/k7bckv80XDg6t7iPlmjo4dK+usp5SncicP5uWxSIoTHOpsDQ/RNz0flJHJ7hkl4IggibEyApurueV3DqKD4KMkQofEsvvih2pkY8IMOvQKyTIsS2ZlHd+lD63e/ruXlxJr2abz769sthLC2zTx4dOr0joWcOd/ZF7irQrW9P9GNqE4Avv/zys88+Q27fEXiMsxGQdL/EE6DTgBPb9tfn71z9jEQ1OKnLLccqykl+WKoIrefm1ZV91FrtA9HJzq1QINZVEQLKvXsjIvv07tB3Jn/6XBQeLQwUayHc7HuCDT1OB0EuKL7jIeKYxc+obZ999tmTJ0+Ktq1usBlnzeDpPuhQdSvklNLEIQNLcdvjlD565vO05Zb8unLqCE0WoVvf1tV8p3SnIcvy999/3woFYt0WIcaY4zik1MuqGWOKoqQVSYf+9Vj8XHc/bHecDceH3Jm0i3sxezEwj1iWheTW1DwgNM46QdV9sJ+Ktkymb9MJN/NX0tmFOV+H/vV4eJmRjs6jQ6eP0IQsxZ4Chf71lf7jsT4yuu0AABDOSURBVHnz77///pNPPsE5e+zTcRFiZc/mmZfIvbfVpw+J5pS8c2ILdy7urXSUnkIQBJqmReN8p0wOMziNszawdR9s3jCM0i98yyqODf2byf8MxbM81xaDDmmalthCqL47wQNLylKwW99++biUhRBy3Da+qG1Pnjxpr4PYNRFi26i5lOvZs45nhw2MD6pz59PLnCfiRBf3zmYzy7IaP3ErEShG2BmW2E7sTwOtcdYDwu4HQaAoiizLJW4wz7rJN1za42eifrOJjkw8dG7FjssVMZ1OS8+vlEIQBDB7OI7TagexgyLEtrN8ekFB3jdJXPPcAjuc729dDP3rsXiW82xQ4N///venn376u9/9brlcFm5kRYBx7wdnlmVhOCn5IJiNswbQdh/sqpQlosyrQuF+7mhnMezxerzROAU4aMCyrCAIImcRoeO1WCzA1Y4mKFT3NWTQFxECYINO4U1baWueDxw6MSEDsPW//e1vX3755YliWS5g3GkeK4z8+lt1LPiNs1Iwdx+Sz6dvpTQMI90fAgcxpjo+lXJv0lqtVoqi/OEPf/j9739fSkKldBKXlg/PVzjolwix2JRawJepKEsWRf2R2wJiqShKs1LkeZ5hGISQ7AmiFQ5XK4yzOpB3P/LiC8/vaZXZEXB0xX3NKtSIHnOc+Ww2+8UvfpFYQ9QsIJCJE1ql94uXSO9ECADHwTCM/PloWEottxlBEFBKB4PB/von/Go0GsmyXH/2eTabKYoC/ulBI7YsC+2JIBEtMs4qwN/9+LJogZfn8PoPn5hwsGFRDRGSdFxUp5o2SLMWydDQUxFijK1WK7AtTdPyBBzT6bTE2Db/06HgBwr8qg44ZrMZtApqr3P6UKBYlTbsdNplnKXTlu7HF2COeuFoNKpCGKAYJx6iRY6joihNJQDyt8FxnDqv1ytGf0UIiL7O0WhkWVaGHWuadnokvlqt4HCnY+Ow6IVVqFFce7I/hESgXqPE9lQB/hZWSou6D5HHUQMENk6U2wxw/tJuTgmCAMrP4A9qu0EGhip8OHlc5yo+mdLpuwhF7EzEs9lsxxc7xdXyPA9OsyeEaJqWP8jYZ1+Nir1VEAQnak8cVJUUibTaOE+ndd2PUgV5Ag7HccqKxVerFaTBc27EjgaRLMvVqdHOUD3qKdgu896Hi9AusFMHBANup5/NZv/973+PdShAeBRFIYTAvrxTtGcfUCN4f0KIoiiGYVBKHcfxtjDGFosF/NtxHMibw2IPvKSsYWMYBrYF2x26YZyFaWn3gyDIkwA4fVVyx7cr4FFVoUaluIng9Z7emOrgIpQKxApwTxQh5MmTJyAkXjrxv4djPxzHqcENCYLA87zpdEophePooWAG9A/+q2kapXQ6nXqeV3qT8BeDdsw4j6Xt3Y/nseEyybhOyLJcQDZWq5XjOLB9sMQsd1yNIqcwp/e5Wq3AeS0rRcEYo5Qi38nHRSgX0+n06uoqPsWnQSktnCJrL57nIa9N6LBx5qEz3Y9cw7gg5S9EXiwWkfAk6lmJ7YTcA8wYhBBILUbuIAA+a+Qywt9AYFdWnUUbxyYXoQTAYppuBV7wr3922Djz0MnugyD9+c9//vnPfw65h2wHcTAYQD0q5ANqbi1EOVFiPCKePK8C/HVDXIRy0WA5ZltAvi2uw8aZhw53P9ohkJEnB5Cvz1dH68YmF6EEGj+8AD/IP6IOG2ceOtx9nqU4SOvGJhehBJB/ixhA/hF12Djz0OHu46/MbBzkHxEXoVwgn2Ex0DpD7xUd7j4fmwdBHixyEcoFN/SDtM7Qe0WHu8/H5kGQV2lzEcoFN/SDcBHCTIe7z8fmQZBXaXMRygU39INwEcJMh7vPx+ZBuAh1AW7oB+EihJkOd5+PzYNwEeoC3NAPwkUIMx3uPh+bB4ELKZpuRSpchHLBDf0gXIQw0+Hu87F5EB4JdQFu6AdBfqhEh40zDx3uPh+bB+Ei1AW4oR8E+UfUYePMQ4e7j9zwMID87mMuQrnghn6Qiu5XLosOG2ceOtx9PjYP0rpUORehBPBfDNU4yL995M2rmg53n4vQQbgIdQHk32LjLBYLzOU3rNPGmYcOdx8uFG66FahB7kNzEcpFiZfYdxLkSWfWaePMQ4e7j/xMGgwUu3m2NrgI5cLzPFmWm24FXvBHih02zjx0uPvIS78wwO8T6gjIv8hmURQFc7zPum6cB+lw9/Hf6tss+D8fLkJ5Qb4PplkIIcivrey2cR6k293nDmIGbUyVcxFKpobUc+g7E+mcEEKIIKrfuv7t9jdr73oiCYQQQkT1leuHlbbjSJAfCgJ02zgP0u3ucwcxA8uyWpcq5yKUTOXLQpsbXbqi3pqxW//ma0kgRJy4m5Cx2yV9IQgX5nzN2HpuXgjkme5+qLAlR0IpNQyj6VYcoNvGeZBud5/XJmQgyzJyheYidARVJp3Ctf315EFaPnrmc0JE3d2wcG4OhTPdvbv/w7k5FMjQ9NBEQ7IsI18QYj0wzmy63X1eN5QB/lwlF6EjqHFHwp1PL4kwttch86lEyIMIgT7BrxCwWq3wWznrgXFm0/nut8II66cV8sxF6Ag8z6urzuS9rT4VVHvNGFvbqkDu/83YNki6pP5d1hvUxXQ61TSt6VYcpvPGmU3nu69p2nQ6bboV6LAsC3+ikovQcdSTegqX9OLsBV1CYcJ7W31KyFCl801UvIAmEmpFLo71wzgz6Hz3Z7MZ/uqY+hkMBphPdAS4CB1HHUcnhG/pxRePSg82c6oOCSGEDFX9TyKJB0ZNEgRBW9IgfTDODPrQ/dFohPlcgPppizBzETqOIAgqdi7Wc/Pqyl6mhDnh2h7jqY5rRV0c0AfjzKAP3W+RNdaDYRj4c3GMi1ABLMuqzNZvfVtXzTeb5N+Gm/krSRBE/SblD2oF9LgtvmdPjDONPnQfamSQb5qujerd5dLgInQ0cAxGBTmoXQUK/esr/cf7tNvGs01VJOfSxEGyVZVSinwndpyeGGcaPek+P1E7okXDk4tQERRFKbsU59a3X4pkh6eq/Z7dufoZnKHwzWs0ZyW0KwxifTLORHrS/VYc3lEPLVoh4yJUBFjxa8WCfEW0yM8C+mOcifSn+6PRqBXlmpXSrqtnuAgVRFGUViz6VQEk31uRbo7olXHu05/uT6fTFs2/FdGiMIhxESoMrAy16JsukTYKcK+Mc5/+dB8SxchPS6uUDmQpuAjlZTabVVOhgJqW9rpvxrlDr7rfUhMthTY6x1yETkLTtFYcWlMW7XUze2iccfrW/b4NzAhN01q3WYqL0EnApNyfhdD2ju0eGmecvnU/CIIeVijA4ZatCwG5CJ0KfPF92CLnOE4bTRzop3FG9LD7/RmYAOhuG09x5SJUApZltWslsABtzDXH6a1xAv3sfh8GZoRhGJ3JUnARKoIsy60rGMtPEARt72CfjZP1tftgt304Q6HVtRhchMphsVi0dMU+D4qitNTJiuizcbIed3+xWLRuT9uxtLdcCOAiVBrgjHTP3A3DkGW5pU5WRM+Ns8/dn06nHT7fBKK91lXExeEiVCaU0g7M13G6oUCs98bZ8+6DGTfdivLpgAIxLkKlA+bejZocwzA6E9v13Dh73v1uTNb7aJrWAXHlIlQ+HZi7gyDoTAwE9Nw4e9591sUtfZ0ZoVyEKgG21LS0oBncxm7Yd0TPjbPn3QegeqgD8VAQBIqidGaEchGqCtCh1pU1Q3lFBwbqDj03zp53P2KxWLQ9Lwc+oqIo3VAgxkWoUlarFYQUrUjNBUFgWVaraz0z6Llx9rz7cVo9iVcpouHG+0GX/kT9uyNf+I5eXOrX3ubwXybDRahyKKWDwQD5cRpg3IqiHCqpuPXdf32nSwJc/Sqqpj333W90+31NDS1Kz42z593fAZY8W+dvUUoJIcftvQ199/X/0aVzQuB2ZtP23rqTr+31zhXNt779UhSkyc393c3hkl4I0RXPz03vY8LfE1F3N4yFG4+q4lPJfFNMh7gI1QHcOqwoCs6QCIz7sExu5lQdEjJUTdvbhIwxtnljSueEXB7vPdVNz42z591PJMo84w+JVqsVLAIdM4GANghEVE0bwpRwM38lCYRI1N/50yW9EJ7p7oftDz64+ueifpMmKluJAhFijDG2udHFpxf0bZjykgy4CNVH5MjgMfojjBv0Rrgw5+v4j0PPHA5Nr4Dp1UvPjbPn3U8DVviR30MarS4fM2/c640gvZpv4oPzo2d+MTTnj8fre1t9Kqh2NLDDJb04e0GXtynv/ZZe/EYUnz4SIRau7bEgjPdirMNwEaoVmPThsNtmpWi1WsEKUD7j/uDqzwg5T/B01vZ4bK8TX4SJnhtnz7ufDczymqbh8Q6BIAg0TStSZ7u50UWBCPtCEq7tr8aPk+ehZw7JU/Xhh+9t9SkhhAiS/t2P3mZnxK/n5uVQdzx6+ViEGFvbqiDsKdxhuAg1gOd5iqIMBoNGoqLVamUYBiHEMIycm2pDzxwSQtoQ8aTRc+PsefcPEk33eDYSwVUUhaTxo2c+JySnHtz59DIhox767utvVFF4nPwIN+5kKL2ab279fRFi76h0tp/rOwgXocbwPC8Sg3qyAY7jgPhZlnXMmQ5H2TRSem6cPe9+TmDttvFEheM40IyCdRPh3BwKSdUEiWxcXSRnupu4qgtJeHHi3q8B3+jS/9r+7Va6dkTova0+TX2rdLgINcxqtaKUjkYjWZYdx6nC9E9+xMbVRfIoYG8fPTfOnnf/KOKJijrP3wqCAM5aPfVO2DtXPyMk7/JMpgjdZ0FE3d2wcGmPX2yLFxJF6MBbpcFFCAuO42iaRgiBm3tms9kpgrRarRzHMQxjNBpBCdAJwRaI0JlE3xVuT+P03Dh73v0C1JmoWCwWUDKuKEoJzwIRyluzunF1MUux1rYqiLq7YT6VSBIP+TcuQl3B8zzLsmRZJoRAYTeldDqdep6XaKBBEMCvKKVwleRgMCCEaJo2nU7LKAoPN+5EJES4oMvw8c/n/5i8LlKUWT89N86ed78wURYBcnTlbrEAT7FQhjybtDKi9fzVX1/vliqkrAltCT1zGKXjdl/F14R6wGKxmM1mlFLDMKCWOtEXURRFURTLsiilnueVn0MIl/Z4SIggqt+6/i1jjIW+Syfq1bXfCgnqvXH2vPunE88rgHvned6xuQrwF3feqookfOhfj0WBkKH66n73aei7VB9f2cv98bpTHRf67mv6L9e/3e40+jy2fygiSYR4dVzfqH3hdO3Zpipud1GLqvnabYsCsd4bZ8+7XyJRoltRlMgF1DSNUhrPWIDYwA/hjyE/AX9celCVwMazTVW8H66CqH6TPl4f7RPaClh0wkLi/ot9EeL7hDicTHpunD3vfnVEwU1cb4AdZcJ8x9jeiQnHw09M4HCy6blx9rz7nEOEm/kr6ezh7LjjXuw7E0nkZ8dxOFn03Dh73n1ODvgp2hxOlfTcOHvefQ5muAhxekHPjbPn3edghosQpxf03Dh73n0OZrgIcXpBz42z593nYIaLEKcX9Nw4e959Dma4CHF6Qc+Ns+fd52CGixCnF/TcOHvefQ5muAhxekHPjbPn3edghosQpxf03Dh73n0OZrgIcXpBz42z593nYIaLEKcX9Nw4e959Dma4CHF6Qc+Ns+fd52CmZBHicNBy2khpNz3vPgcz+8bJjZXD6RpNOwAcTha75trIIOFwOBwOh3ER4nA4HE6DcBHicDgcTmNwEeJwOBxOY/x/c3lnqIdFDAgAAAAASUVORK5CYII=" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for three circles and a rectangle (<em>U</em> need not be seen)</span></p>
<p><span><em><strong>(A1)</strong></em> for 5</span></p>
<p><span><em><strong>(A1)</strong></em> for 3, 8 and 12</span></p>
<p><span><em><strong>(A1)</strong></em> for 16, 26 and 29 <strong>OR</strong> 32, 46, 54 placed outside the circles. <em><strong>(A4)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept answers given as decimals or fractions.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>100 – (16 + 26 + 29) – (8 + 5 + 3 + 12) <em><strong>(M1)</strong></em></span></p>
<p><span>100 – 71 – 28</span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct expression. Accept equivalent expressions, for example 100 – 71 – 28 or 100 – (71 + 28).</span></p>
<p> </p>
<p><span>= 1 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><span><strong>Note:</strong> Follow through from their Venn diagram but only if working is seen.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16 + 26 + 29 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 16, 26, 29 seen.</span></p>
<p> </p>
<p><span>= 71 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><span><strong>Note:</strong> Follow through from their Venn diagram but only if working is seen.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16 + 3 + 26 <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their 16, 3, 26 seen.</span></p>
<p><br><span>= 45 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their Venn diagram but only if working is seen.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>True <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>100 – (1 –16) = 83 <em><strong>(R1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>46 + 54 – 17 = 83 <em><strong>(R1)</strong></em><strong>(ft)</strong> </span></p>
<p><span><strong>Note:</strong> Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from their Venn diagram.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>28% of 120000 <em><strong>(M1)</strong></em></span></p>
<p><span>= 33600 <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{% error}} = \frac{{(34000 - 33600)}}{{33600}} \times 100\)</span><span> </span><span> <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for 28 seen (may be implied by 33600 seen),</span> <span>award <em><strong>(M1)</strong></em> for correct substitution of <strong>their</strong> 33600 in the percentage </span><span>error formula. If an error is made in calculating 33600 award a</span> <span>maximum of <em><strong>(M1)(A0)(M1)(A0)</strong></em>, the final accuracy mark is lost.</span></p>
<p><span> </span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(\frac{{34000}}{{120000}} \times 100\)</span> <span> <em><strong>(M1)</strong></em></span></p>
<p><span>= 28.3(28.3333…) <em><strong>(A1)</strong></em></span></p>
<p><span>\({\text{% error}} = \frac{{(28.3333... - 28)}}{{28}} \times 100\)</span> <span> <em><strong>(M1)</strong></em></span></p>
<p><span>= 1.19% (1.19047...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> % sign not required. Accept 1.07 (1.0714…) with use of 28.3.</span> <span>1.18 with use of 28.33 and 1.19 with use of 28.333.</span> <span>Award <em><strong>(G3)</strong></em> for 1.07, 1.18 or 1.19 seen without working.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and </span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and </span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and</span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and </span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and </span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was accessible to the great majority of candidates. The common errors were:</span></p>
<ul>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of a bounding rectangle in (a);</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the lack of subtraction for the entries in the disjoint regions of the type \(A' \cap B' \cap C\) </span><span style="font-size: medium; font-family: times new roman,times;">and the subsequent total exceeding 100%;</span></li>
<li><span style="font-size: medium; font-family: times new roman,times;">the <strong>incorrect</strong> interpretation of “either ...or” as “exclusive or”. It is of the utmost </span><span style="font-size: medium; font-family: times new roman,times;">importance to note that the ambiguity of the “or” statement will be removed and</span><span style="font-size: medium; font-family: times new roman,times;">“exclusive or” signalled by the phrase “either ...or....<strong>but not both</strong>”. Otherwise, </span><span style="font-size: medium; font-family: times new roman,times;">“inclusive or” must always be assumed.</span></li>
</ul>
<p><span style="font-size: medium; font-family: times new roman,times;">A number of candidates were unable to interpret the percentage error question correctly and </span><span style="font-size: medium; font-family: times new roman,times;">scored 0/4. This was somewhat disappointing.</span></p>
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A survey of 100 families was carried out, asking about the pets they own.</span> <span style="font-size: medium; font-family: times new roman,times;">The results are given below.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">56 owned dogs <em>(S)</em></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">38 owned cats <em>(Q)</em></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">22 owned birds <em>(R)</em></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">16 owned dogs and cats, but not birds</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">8 owned birds and cats, but not dogs</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">3 owned dogs and birds, but not cats</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">4 owned all three types of pets</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to represent this information.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of families who own no pets.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the percentage of families that own exactly one pet.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A family is chosen at random. Find the probability that they own a cat, given that they own a bird.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt> <em><strong>(A1)(A1)(A1)(A1)(A1)</strong></em></span></p>
<p> </p>
<p><span><strong> </strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for rectangle (<em>U</em> <em>not required</em>), <em><strong>(A1)</strong></em> for 3 intersecting circles, <em><strong>(A1)</strong></em> for 4 in central intersection, <em><strong>(A1)</strong></em> for 16, 3, 8 and <em><strong>(A1)</strong></em> for 33, 10, 7 <strong>(ft)</strong> if subtraction is carried out, or for <em>S</em>(56), <em>Q</em>(38) and <em>R</em>(22) seen by the circles.</span></p>
<p><span> </span></p>
<p><em><strong><span>[5 marks]</span></strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>100 − 81 <em><strong>(M1)</strong></em></span></p>
<p><span>19 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p> </p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their total from 100.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(33 +10 + 7\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for adding their values from (a).</span></p>
<p><br><span>\(\left( {\frac{{50}}{{100}}} \right) \times 100{\text{ }}\% \) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>50 % (50) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>P (own a cat given they own a bird) \( = \frac{{12}}{{22}}\left( {0.545,\frac{6}{{11}}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the numerator, <em><strong>(A1)</strong></em><strong>(ft)</strong> for the denominator.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Most candidates began the paper well by correctly drawing the Venn diagram and answering parts (b) and (c) correctly.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"><span style="font-size: medium; font-family: times new roman,times;">Conditional probability has proved difficult for many candidates; only a very small part of the candidates scored full marks for this part.</span></span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Pam has collected data from a group of 400 IB Diploma students about the Mathematics course they studied and the language in which they were examined (English, Spanish or French). The summary of her data is given below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A student is chosen at random from the group. Find the probability that the student</span></p>
<p><span>(i) studied Mathematics HL;</span></p>
<p><span>(ii) was examined in French;</span></p>
<p><span>(iii) studied Mathematics HL and was examined in French;</span></p>
<p><span>(iv) did not study Mathematics SL and was not examined in English;</span></p>
<p><span>(v) studied Mathematical Studies SL given that the student was examined in Spanish.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Pam believes that the Mathematics course a student chooses is independent of the language in which the student is examined.</span></p>
<p><span>Using your answers to parts (a) (i), (ii) and (iii) above, state whether there is any evidence for Pam’s belief. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Pam decides to test her belief using a Chi-squared test at the \(5\% \) level of significance.</span></p>
<p><span>(i) State the null hypothesis for this test.</span></p>
<p><span>(ii) Show that the expected number of Mathematical Studies SL students who took the examination in Spanish is \(41.3\), correct to 3 significant figures.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down</span></p>
<p><span>(i) the Chi-squared calculated value;</span></p>
<p><span>(ii) the number of degrees of freedom;</span></p>
<p><span>(iii) the Chi-squared critical value.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>State, giving a reason, whether there is sufficient evidence at the \(5\% \) level of significance that Pam’s belief is correct.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{100}}{{400}}{\text{ }}\left( {\frac{1}{4}{\text{, }}0.25{\text{, }}25\% } \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(ii) \(\frac{{90}}{{400}}{\text{ }}\left( {\frac{9}{{40}}{\text{, }}0.225{\text{, }}22.5\% } \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span> </span></p>
<p><span>(iii) \(\frac{{20}}{{400}}{\text{ }}\left( {\frac{1}{{20}}{\text{, }}0.05{\text{, }}5\% } \right)\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p> </p>
<p><span>(iv) \(\frac{{120}}{{400}}{\text{ }}\left( {\frac{3}{{10}}{\text{, }}0.3{\text{, }}30\% } \right)\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span> </span></p>
<p><span>(v) \(\frac{{30}}{{110}}{\text{ }}\left( {\frac{3}{{11}}{\text{, }}0.273{\text{, }}27.3\% } \right)\) (\(0.272727 \ldots \)) <em><strong>(A1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator. Accept \(0.27\), do not accept \(0.272\), do not accept \(0.3\).</span></p>
<p><span> </span></p>
<p><span><em><strong>[8 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{{20}} \ne \frac{1}{4} \times \frac{9}{{40}}\) <em><strong>(R1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> The fractions must be used as part of the reason. Follow through from (a)(i), (a)(ii) and (a)(iii).</span></p>
<p> </p>
<p><span>Pam is not correct. <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Do not award <em><strong>(R0)(A1)</strong></em>. Accept the events are not independent (dependent).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) The mathematics course and language of examination are independent. <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Accept “There is no association between Mathematics course and language”. Do not accept “not related”, “not correlated”, “not influenced”.</span></p>
<p><br><span>(ii) \(\frac{{110}}{{400}} \times \frac{{150}}{{400}} \times 400{\text{ }}\left( { = \frac{{110 \times 150}}{{400}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span> \( = 41.25\) <em><strong>(A1)</strong></em></span></p>
<p><span> \( = 41.3\) <em><strong>(AG)</strong></em></span></p>
<p><span><strong>Note:</strong> \(41.25\) <strong>and</strong> \(41.3\) must be seen to award final <em><strong>(A1)</strong></em>.</span></p>
<p><span> </span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(7.67\) (\(7.67003 \ldots \)) <em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept \(7.7\), do not accept \(8\) or \(7.6\). Award <em><strong>(G1)</strong></em> if formula with all nine terms seen but their answer is not one of those above.</span></p>
<p> </p>
<p><span>(ii) \(4\) <em><strong>(G1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(iii) \(9.488\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Accept \(9.49\) or \(9.5\), do not accept \(9.4\) or \(9\). Follow through from their degrees of freedom.</span></p>
<p><span> </span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(7.67 < 9.488\) <em><strong>(R1)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>\(p = 0.104 \ldots , p > 0.05\) <em><strong>(R1)</strong></em></span></p>
<p><span>Accept (Do not reject) \({H_0}\) (Pam’s belief is correct) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Follow through from part (d). Do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The simple probabilities beginning this question were successfully attempted by the great majority. Most errors in the latter parts occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table. Probability questions in this course are, in the main, contextual and the reliance of formulas is not always beneficial to the candidates. Only the best candidates realized the significance of part (b) as a link to the chi-squared test.</span></p>
<p><br><span style="font-size: medium; font-family: times new roman,times;">This was well attempted by the majority, the weakness being the sole reliance of the calculator to calculate expected value. However, there still remains confusion between critical and <em>p</em>-values as the basis for accepting the null hypothesis.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The simple probabilities beginning this question were successfully attempted by the great majority. Most errors in the latter parts occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table. Probability questions in this course are, in the main, contextual and the reliance of formulas is not always beneficial to the candidates. Only the best candidates realized the significance of part (b) as a link to the chi-squared test.</span></p>
<p><br><span style="font-size: medium; font-family: times new roman,times;">This was well attempted by the majority, the weakness being the sole reliance of the calculator to calculate expected value. However, there still remains confusion between critical and \(p\)-values as the basis for accepting the null hypothesis.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The simple probabilities beginning this question were successfully attempted by the great majority. Most errors in the latter parts occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table. Probability questions in this course are, in the main, contextual and the reliance of formulas is not always beneficial to the candidates. Only the best candidates realized the significance of part (b) as a link to the chi-squared test.</span></p>
<p><br><span style="font-size: medium; font-family: times new roman,times;">This was well attempted by the majority, the weakness being the sole reliance of the calculator to calculate expected value. However, there still remains confusion between critical and \(p\)-values as the basis for accepting the null hypothesis.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The simple probabilities beginning this question were successfully attempted by the great majority. Most errors in the latter parts occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table. Probability questions in this course are, in the main, contextual and the reliance of formulas is not always beneficial to the candidates. Only the best candidates realized the significance of part (b) as a link to the chi-squared test.</span></p>
<p><br><span style="font-size: medium; font-family: times new roman,times;">This was well attempted by the majority, the weakness being the sole reliance of the calculator to calculate expected value. However, there still remains confusion between critical and \(p\)-values as the basis for accepting the null hypothesis.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The simple probabilities beginning this question were successfully attempted by the great majority. Most errors in the latter parts occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table. Probability questions in this course are, in the main, contextual and the reliance of formulas is not always beneficial to the candidates. Only the best candidates realized the significance of part (b) as a link to the chi-squared test.</span></p>
<p><br><span style="font-size: medium; font-family: times new roman,times;">This was well attempted by the majority, the weakness being the sole reliance of the calculator to calculate expected value. However, there still remains confusion between critical and \(p\)-values as the basis for accepting the null hypothesis.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Leanne goes fishing at her favourite pond. The pond contains four different types of fish: bream, flathead, whiting and salmon. The fish are either undersized or normal. This information is shown in the table below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of fish in the pond.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Leanne catches a fish.</span></p>
<p><span>Find the probability that she</span></p>
<p><span>(i) catches an undersized bream;</span></p>
<p><span>(ii) catches either a flathead or an undersized fish or both;</span></p>
<p><span>(iii) does not catch an undersized whiting;</span></p>
<p><span>(iv) catches a whiting given that the fish was normal.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></p>
<p><span><strong>Copy and complete</strong> the probability tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Calculate the probability that it is windy and Leanne catches a fish on a particular day.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Calculate the probability that Leanne catches a fish on a particular day.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your answer to part (e) to calculate the probability that Leanne catches a fish on two consecutive days.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>Leanne notices that on windy days, the probability she catches a fish is 0.1 while on non-windy days the probability she catches a fish is 0.65. The probability that it will be windy on a particular day is 0.3.</span></span></p>
<p><span>Given that Leanne catches a fish on a particular day, calculate the probability that the day was windy.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>90 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{3}{{90}}(0.0\bar 3,{\text{ }}0.0333,{\text{ }}0.0333...,{\text{ }}3.\bar 3\% ,{\text{ }}3.33\% )\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> For the denominator follow through from their answer in part (a).</span></p>
<p><br><span>(ii) \(\frac{{53}}{{90}}(0.5\bar 8,{\text{ }}0.588...,{\text{ }}0.589,{\text{ }}58.\bar 8\% ,{\text{ }}58.9\% )\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for the numerator. <em><strong>(A1)</strong></em><strong>(ft)</strong> for denominator. For the denominator follow through from their answer in part (a).</span></p>
<p><br><span>(iii) \(\frac{{72}}{{90}}{\text{(0.8, 80}}\%)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for the numerator, (their part (a) –18) <strong><em>(A1)</em>(ft)</strong> for denominator. For the denominator follow through from their answer in part (a).</span></p>
<p><br><span><span>(iv) </span><span>\(\frac{{24}}{{48}}(0.5,{\text{ 50}}\% )\)</span> <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span> </span></p>
<p><span><span><em><strong>[7 marks]</strong></em></span> </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> </span></span><span> <em><strong><span>(A1)(A1)(A1)</span><br></strong></em><br><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for each correct entry. Tree diagram must be seen for marks to be awarded.<em><strong><br></strong></em></span></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.1 = 0.03\left( {\frac{3}{{100}}} \right)\)</span><em><strong><span> (M1)(A1)(G2)</span></strong></em></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct product seen.</span><em><strong><span><br></span></strong></em></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.1+ 0.7\times0.65\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for \(0.7\times0.65\) (or 0.455) seen, <em><strong>(M1)</strong></em> for adding their 0.03. Follow through from their answers to parts (c) and (d).</span></p>
<p><br><span>\( = 0.485\left( {\frac{{485}}{{1000}},\frac{{97}}{{200}}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their tree diagram and their answer to part (d).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.485 \times 0.485\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(0.235\left( {\frac{{9409}}{{40000}}{\text{, }}0.235225} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their answer to part (e).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{0.03}}{{0.485}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for substituted conditional probability formula, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their (d) as numerator and their (e) as denominator.</span><br><br><span>\(0.0619\left( {\frac{{6}}{{97}}}\text{, 0.0618556...} \right) \) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their parts (d) and (e).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(a) Most candidates found this correctly although a few wrote 180 instead of 90.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(b) This was also answered well. The main errors were putting 65/90 in part (ii) and</span> <span style="font-size: medium; font-family: times new roman,times;">24/90 in part (iv).</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(c) The tree diagram was completed correctly in most scripts. It appears that some </span><span style="font-size: medium; font-family: times new roman,times;">candidates may have answered this on their question paper and this was not sent to </span><span style="font-size: medium; font-family: times new roman,times;">the scanning centre with the answer papers.</span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(d) Many answered this correctly. Some added instead of multiplying.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(e) Surprisingly well answered. Again some added and multiplied in the wrong place.</span></p>
<p> </p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(f) Most candidates added here and then divided by 2 rather than multiplying.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(g) This was badly done with very few correct answers seen.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A geometric sequence has second term 12 and fifth term 324.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Consider the following propositions</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em>: The number is a multiple of five.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>q</em>: The number is even.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;"><em>r</em>: The number ends in zero.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of the common ratio.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the 10<sup>th</sup> term of this sequence.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The <em>k</em><sup>th</sup> term is the first term which is greater than 2000. Find the value of <em>k</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write in words \((q \wedge \neg r) \Rightarrow \neg p\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the statement “If the number is a multiple of five, and is not even then it will not end in zero”.</span></p>
<p><span>Write this statement in symbolic form.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">ii, b, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the statement “If the number is a multiple of five, and is not even then it will not end in zero”.</span></p>
<p><span>Write the contrapositive of this statement in symbolic form.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, b, ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>u</em><sub>1</sub><em>r</em><sup>4</sup> = 324 <em><strong>(A1)</strong></em></span></p>
<p><span><em>u</em><sub>1</sub><em>r</em> = 12 <em><strong>(A1)</strong></em></span></p>
<p><span><em>r</em><sup>3</sup> = 27 <em><strong>(M1)</strong></em></span></p>
<p><span><em>r</em> = 3 <em><strong>(A1)(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award at most <em><strong>(G3)</strong></em> for trial and error.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>4 × 3<sup>9</sup> = 78732 <strong>or </strong>12 </span><span><span>× </span>3<sup>8</sup> = 78732 <em><strong>(A1)(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for <em>u</em><sub>1</sub> = 4 if<em> n</em> = 9 , <strong>or</strong> <em>u</em><sub>1</sub> = 12 if <em>n</em> = 8, <em><strong>(M1)</strong></em> for correctly substituted formula.</span></p>
<p><span><strong>(ft)</strong> from their (a).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>4 × 3<sup><em>k</em>−1</sup> > 2000 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution in correct formula. Accept an</span> <span>equation.</span></p>
<p><br><span><em>k</em> > 6 <em><strong>(A1)</strong></em></span></p>
<p><span><em>k</em> = 7 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> If second line not seen award <em><strong>(A2)</strong></em> for correct answer. <strong>(ft)</strong> from</span> <span>their (a).</span></p>
<p><span>Accept a list, must see at least <strong>3 terms</strong> including the 6<sup>th</sup> and 7<sup>th</sup>.</span></p>
<p><br><span><strong>Note:</strong> If arithmetic sequence formula is used consistently in parts (a), (b)</span> <span>and (c), award <em><strong>(A0)(A0)(M0)(A0)</strong></em> for (a) and <strong>(ft)</strong> for parts (b) </span><span>and (c).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If the number is even and the number does not end in zero, (then) the number is not a multiple of five. <em><strong>(A1)(A1)(A1)</strong></em><br></span></p>
<p><span> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em> for “the number is even and the number does not end in zero”, <em><strong>(A1)</strong></em> for the number is not a multiple of 5.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\((p \wedge \neg q) \Rightarrow \neg r\) <em><strong>(A1)(A1)(A1)(A1)</strong></em></span></p>
<p><span><em><strong>(A1)</strong></em> <em>for</em> \(\Rightarrow\), <em><strong>(A1)</strong></em> <em>for</em> \(\wedge\), <em><strong>(A1)</strong></em> <em>for</em> p and \(\neg q\), <em><strong>(A1)</strong></em> <em>for</em> \(\neg r\)</span></p>
<p><br><span><strong>Note:</strong> If parentheses not present award at most <strong><em>(A1)(A1)(A1)(A0)</em></strong>.</span></p>
<p><span> </span></p>
<p><em><strong><span>[4 marks]</span></strong></em></p>
<p><br><span><br></span></p>
<div class="question_part_label">ii, b, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(r \Rightarrow (\neg p \vee q)\) <strong>OR</strong> \(r \Rightarrow \neg (p \wedge \neg q)\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></span></p>
<p><span><span><br> </span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for reversing the order, <strong><em>(A1)</em></strong> for negating the statements on both sides.</span></p>
<p><span>If parentheses not present award at most <strong><em>(A1)</em>(ft)<em>(A0)</em></strong>.</span></p>
<p><span>Do not penalise twice for missing parentheses in (i) and (ii).</span></p>
<p><span> </span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">ii, b, ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">An easy ratio to find and the majority of candidates found <em>r</em> = 3, though many had trouble showing the appropriate method, thus losing marks.</span></p>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">A fairly straightforward part for most candidates.</span></p>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The majority found <em>k</em> − 7; many without supporting work which lost them a mark. Where candidates had difficulty in this part, it was generally a case of poor algebraic skills.</span></p>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question on logic was straightforward for most candidates who scored full marks for parts (a) and (b) (i). A few omitted the brackets in part (b).</span></p>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question on logic was straightforward for most candidates who scored full marks for parts (a) and (b) (i). A few omitted the brackets in part (b).</span></p>
<div class="question_part_label">ii, b, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Very poorly answered with many candidates scoring just one mark. The main error was to open the bracket and not use the “or”.</span></p>
<div class="question_part_label">ii, b, ii.</div>
</div>
<br><hr><br><div class="specification">
<p>In a company it is found that 25 % of the employees encountered traffic on their way to work. From those who encountered traffic the probability of being late for work is 80 %.</p>
<p>From those who did not encounter traffic, the probability of being late for work is 15 %.</p>
<p>The tree diagram illustrates the information.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>The company investigates the different means of transport used by their employees in the past year to travel to work. It was found that the three most common means of transport used to travel to work were public transportation (<em>P </em>), car (<em>C </em>) and bicycle (<em>B </em>).</p>
<p>The company finds that 20 employees travelled by car, 28 travelled by bicycle and 19 travelled by public transportation in the last year.</p>
<p>Some of the information is shown in the Venn diagram.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="specification">
<p>There are 54 employees in the company.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>a</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the value of <em>b</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic and was late for work.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee was late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Use the tree diagram to find the probability that an employee encountered traffic given that they were late for work.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>x</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of <em>y</em>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of employees who, in the last year, did not travel to work by car, bicycle or public transportation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(n\left( {\left( {C \cup B} \right) \cap P'} \right)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>a</em> = 0.2 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>b</em> = 0.85 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award <em><strong>(M1)</strong></em> for a correct product.</p>
<p>\( = 0.2\,\,\,\left( {\,\frac{1}{5},\,\,\,20\% } \right)\) <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.25 × 0.8 + 0.75 × 0.15 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their (0.25 × 0.8) and (0.75 × 0.15), <em><strong>(M1)</strong></em> for adding two products.</p>
<p>\( = 0.313\,\,\,\left( {0.3125,\,\,\,\frac{5}{{16}},\,\,\,31.3\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award the final <em><strong>(A1)</strong></em><strong>(ft)</strong> only if answer does not exceed 1. Follow through from part (b)(i).</p>
<p><strong><em>[3 marks]</em></strong></p>
<p> </p>
<p> </p>
<p> </p>
<p> </p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{0.25 \times 0.8}}{{0.25 \times 0.8 + 0.75 \times 0.15}}\) <strong><em>(A1)</em>(ft)</strong><strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for a correct numerator (their part (b)(i)), <strong><em>(A1)</em>(ft)</strong> for a correct denominator (their part (b)(ii)). Follow through from parts (b)(i) and (b)(ii).</p>
<p>\( = 0.64\,\,\,\left( {\frac{{16}}{{25}},\,\,64{\text{% }}} \right)\) <strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p><strong>Note:</strong> Award final <strong><em>(A1)</em>(ft)</strong> only if answer does not exceed 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>x</em> =) 3 <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>y</em> =) 10 <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Following through from part (c)(i) but only if their <em>x</em> is less than or equal to 13.</p>
<p><em><strong>[1 Mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>54 − (10 + 3 + 4 + 2 + 6 + 8 + 13) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting their correct sum from 54. Follow through from their part (c).</p>
<p>= 8 <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> only if their sum does not exceed 54. Follow through from their part (c).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>6 + 8 + 13 <em><strong>(M1)</strong></em></p>
<p><strong>Note</strong>: Award (M1) for summing 6, 8 and 13.</p>
<p>27 <em><strong>(A1)(G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p>Consider these three propositions, in which <em>x </em>is a natural number.</p>
<p>\[\begin{array}{*{20}{l}} {p{\text{: }}x{\text{ is a factor of 60}}} \\ {q{\text{: }}x{\text{ is a multiple of 4}}} \\ {r{\text{: }}x{\text{ is a multiple of 5}}} \end{array}\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in symbolic form the compound proposition</p>
<p>“If \(x\) is a factor of 60 then \(x\) is a multiple of 5 or \(x\) is not a multiple of 4.”</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down in words the compound proposition \(\neg r \wedge (p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy </strong>the following truth table and complete the last three columns.</p>
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAhAAAAFBCAYAAAAmOpZGAAAgAElEQVR4Ae3df4xc13UY4LMUoQaxujZUEdWslEYwVTUp4jo2CQcwBJhaVpTdBK0i13JiQHIt1bURyQZq2LsgEf8TCytQJGjAtlxZKQNHioM2LQWnKRCbyW7kovlDwtIJqiAyBTuQImnXLllHXLJKI4n7ihnOUsM7s/uW+2vunfkWWOzcmTvzzv3OfW/OvvfmzUhVVVX4IUCAAAECBAhchsC2y+irKwECBAgQIECgJaCAMBEIECBAgACByxZQQFw2mScQIECAAAEC2zsJRkZGOptuEyBAgAABAgRaAukpk5cUEM0eaYdhc2sWUQwYmAflrflyVlbO5Ku8fKURO4SRimgTIECAAAECtQIKiFoiHQgQIECAAIFUQAGRimgTIECAAAECtQIKiFoiHQgQIECAAIFUQAGRimgTIECAAAECtQIKiFoiHQgQIECAAIFUQAGRimgTIECAAAECtQIKiFoiHQgQIECAAIFUQAGRimgTIECAAAECtQIKiFoiHQgQIECAAIFUQAGRimgTIECAAIFVCyzGued+Pw4f/v147tziqp/Vn46Lce57/zkOf/HbGxKrAqI/WbRUAgQIEChe4LWYn3kw7vtvjfjkZ/9V3HRV7m+p2+Kqn/lwfOZXtsXX73swZuZfW1cGch/tugbnyQQIECBAYHMEFuPciYfjI1/4yfj0J3fHVZuzkE151W2NvXHg0z8ZX/jIw3FiHXtNFBCbkh4vSoAAAQIDLXBuNh757MNx5V0fiHdlv+chzcS2uOpdH4i7rnw4Dvzec7HWAy99LiDOxYnDt0Tza11HRm6Jw08/Fyd+ezJuabXfER/94p/G/FpHlnoV0F6cfzp+e/K2lsfYvY/HH/3mnTEydiBmFoYB4Y2Yf+KT7bmwOyZnTsdFj6Ex6MckfTGe+OiNF9xbzv8v5k88HpO3jMXY5Ews9COk4pe51u3aK3Hi8C/HLYefjnPLGCy+/ETce+P98cTLK+16fu1iDkdG3hH3/tf/Hr952xDlc/6J+GjrPWTkwhxenG+/r1zYrixD2777tXj5iftjbOSX4vCJV1bouhgLT38zjjz57vjwzTdE9xtpAXNg2/Xxzlt/Ko7/+mPx5FrfY6qOn4joaG3VzderuWOfqCL2VHffM1EdeWquOl/9TTV76BeriA9VR0/+7VYF0lpOfwzOV2ef/Xp1dyOqxt1fr549+3p1dvZItSeiiruPVXNbKlBV/TFoDvJ8dWZ6f9Vo7K+mX3qqOnrkD6rpRz9UNe45Vr10fmsR+mewteO8sLRT1fTErqoxcbx6afax6sjxb1WP7ttV3XPs+WqL2dc1+Lxytsbt2tmnqkN7bq8Ozf5Nt8X556tj9+yq9h19doW8nKmePXpP1Yifq+4++kx19uK2dGd197G/7n7NPt6zqfk6M11NNHZVE9Mnq9mjj1bHp79S7WvcVx176e9WHnHrefuqz0x8pGrsO1qdXHYFuLDORHNbdWa5TrnPgaX4mk6nVnaper8vXFIxbGpClw2vnYj4xY6Vpv1GEnuqQ7Nnl33mZjzQF4PWRqNRxZ4j1ezZ9mScO1bdHY2ajcVmCPSeKJuzpPRV23Nhz33VxMR/eNMi7bYF7b7Mgy0YV89FtDaajWrPZyaqiSNPVVu7xvWMaE135pWztW7X/q566dh9VaNzW9DSaG8Tu+7vpDrf/sejUe05tJTHpTeJrf9nrDOyXrc3L19L7x/NQmB/daRXMdYroHax1ZiYrs60irU9yxfRr89Wh3ZGFTsPVbOv93yxqqrynwOvzx6qdq7yfaZXvrr3vKyw02ZTHnrjhfjusRPRmPhM/Ltdb7u4G+mHz38/5mNHXP33t2/KYvN50VfixCO/EZ978t1x6PDHYlfrWNpiLDw7G38U/yRufef1PXaP5RP9hkayeDqe//O5iCefjx13/krbYkOXMLAv9saJw3Fje7fthUOCzcOCy/3eGB994sWLFos/fD7+fH4+nvzutXHnx8s6GeziIHK7sebt2pVx3e33xwNXfiO+evzFN49Nn5uNR79wPD7wqTuWP97eOiZ/KJ7c87k4fPGkvlfi2admI3a+J9759p/ITWnFeNY+p1+LC+8fz8R3d9weH7/4vrLi4mLx5Zn46iM3xFc+fXOMbvup2Pdr/zL+6v6vrX33fjFzYD5+8OP/++ZcW5np0kc7a6deFUbn45tx+/zJo9W+SHahtP8jH4pd10uV7CW7y9qV64q7xzYjGxdesx/zoLnkC3MhqtZ/AJs3vFW9cr8MVhXcujqdbR0efHN39t9WJ49+qIp0HVzXMvrz5Jxytr7tWntPwsVd7u1DupdsI7qNe/432dq7lMc6lUa8cflK5vT5Z6uj+xrVyocX0mia29z3Jnt8m+63d+zN6XjO0nZ7hT0QJcyBC3Mmqp2HZqtld6S0h90rX33eA/FG/Ogvno7jjX1x2+6r25XNQnzv974WR07eEV/5jV+K6/oc4aXl1ia0Tr0Qz/wgYuet74y3t8ba/GjQ4/GFh05E3Lo7fnZ00AGWTBfj3Evfj2fiQ/HAve+N0aW7/d1kgXPx0sm/itj3a3Hvnms2eVnD8vLr3a41z5C/Iz71ge/E/V/6n/HKc0/Egc9FHJq6I25adnPwRpx64fvxg0v2Wr4SJx49Eg/N74xbf+EfD886dW4uTj4Tse+Bu2PPqraf7W3u0/86pu68qWOP79viXb96V7z9kcfi+Ionrfaa1yXNgUbsvPotHePuNZ7e9y07HXt33+h727vXYiFeOftGxOJ8PP3FT8X4vS/Fv/md/XH7dVdu9ALze723vC2ubUS8+uwL8aPF12L+6a/HI3+yEP+o0Yh97/un8Q/zi3iTIvpxzH77eMzve3/cfGNZu1o3CWRrXnbhf8W3H5+LfR9+b9zY563B1gx4K5ayAdu1bT8dt0/++3jHQxPxy5+YimcuOcTbawzb4i1vuzoacTqefeH/xGJzW/ql/xh/8sY/iEa8O973czt6PWkA71uMhdk/jsfnb17m0xE9hrz4Yhz/6rfiPZ+/q+uw6bbr/kVMHvjfrULukk8kbf/pePcHd0W8+uM482qvT8mVMAcW49UzP45XYyx+/oZrCiwg2seIYv7h+OD1fy9GrtgVkz98X/zOyf8SU+PXrWlAPaZH3neN7o6PPXBPxG99MK6//uPxjTM3x7+95S3xp5ezAuQ9wtVF1z7/ofHzN8S13shWZ7YBvS6c/7D2DcgGhDB4L7FB27VtN90RU4eujSdPvv/CcfkVpbbF6Hs+Eg/c3dyU3BDXf+w/xZn3/2rcsv2vh6wob5//0Lgxbrh2Nf+AvhYvf/NQTMQn4tM998D9RNx052fjM09/OR695GOdV8fu2/ZFY/778fwPe3yktog5sGTVeQRgxUnW/WDHUZ0t//hez2NEnQH14Xav4zxbG0b7mHSfzn9ojrX/Blsr3mtpDHqp5H1fLjnLZrvWPhcgh3OKes2cXPLVK7ZV3dfy3ZmcN3HhmUXMgRXi7zX+Xvnq4/967WPel5z/0F3gDN89p+IvvvPdaNz1z2P3qo7fDZ+QERPIV2Dt27XlPzXT+9M0tQY/+sv4zvGxuOu2fzY85z/Uomxgh203xZ1T98Vrj/9h/Nkll4MuYQ4sxrk/+8N4/LX7kvM+Ls+nfwXE4ovxx9/4g5gfqhMF65LT/GKW34ovPxbDddJTHYvHCZQisI7tWnPn3+X8rkiy+HLMfPlr8Vjsjl/42aWPx6/4DA9etsC2uGrXffG7n381vjQ1/eZVkwuYA4vz0zH1pVfj8797X9d5H5fF0Lmrotcuis7HN+r20kdHmstr/fZxd306pq0ySJdbtT9uddEk+nfluL4ZdKH07w4G/bNf65L7nbM8tmtLF1Fqb1tb29hPVMfm6j6kt1b1tT+v3/lae+TpM89XZ09+szp06JvVX/6Pg9XOpfe15t++vLetNAfejPXk0kUL0+Es0+6Vr5Fm36WKo7kLraO5dPdQ/WUQrQsQmQfWhdJWfOtuWRmTr/Lz1b9DGGXZiZYAAQIECBDoEFBAdGC4SYAAAQIECKxOQAGxOie9CBAgQIAAgQ4BBUQHhpsECBAgQIDA6gQUEKtz0osAAQIECBDoEOj6FEbHY24SIECAAAECBFoC6afztqcuaYf08UFv+2iRj3E257h5UN6aLmdl5Uy+ystXGrFDGKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAX6WEAsxsLMgRgbGWldNrh5WdPev7tjcuZ0GveAtBlEMBiQyWwYBAgMmUDXl2n177swmm8kvx4/s/d43DX9rTg4fk1fUtHf67MzuFBQDPs86MvUL36h/V13i+fb8gHI15aTr2uBvfLVxz0Q6xqLJxMgQIAAAQJ9FFBA9BHfogkQIECAQKkCCohSMyduAgQIECDQRwEFRB/xLZoAAQIECJQqoIAoNXPiJkCAAAECfRRQQPQR36IJECBAgECpAgqIUjMnbgIECBAg0EcBBUQf8S2aAAECBAiUKqCAKDVz4iZAgAABAn0UUED0Ed+iCRAgQIBAqQIZXco6D8Jel+vMI7Kti4JBtL6XpX+Xdd+6XA/SkszbsrIpX+Xnyx6IsnIoWgIECBAgkIWAAiKLNAiCAAECBAiUJaCAKCtfoiVAgAABAlkIKCCySIMgCBAgQIBAWQIKiLLyJVoCBAgQIJCFgAIiizQIggABAgQIlCWggCgrX6IlQIAAAQJZCCggskiDIAgQIECAQFkCCoiy8iVaAgQIECCQhYACIos0CIIAAQIECJQl0HUp67LCFy0BAgQIECCwFQLp5f23pwtNO6SPD3rb9dl9D0RzjpsH5a3pclZWzuSrvHylETuEkYpoEyBAgAABArUCCohaIh0IECBAgACBVEABkYpoEyBAgAABArUCCohaIh0IECBAgACBVEABkYpoEyBAgAABArUCCohaIh0IECBAgACBVEABkYpoEyBAgAABArUCCohaIh0IECBAgACBVEABkYpoEyBAgAABArUCCohaIh0IECBAgACBVKCPBcRiLMwciLGRkdZlg5uXNe39uzsmZ06ncQ9Im8GFRJ6Omcndy+T/wrwYm5yJhQHJumEQIEBgEAT6WEBsi9HxqZirqmh+/0ZVnY8z0/ujEbtiYvpU+77m/bNxcPyaQbDuMQYGl6A09sf0mfMduV+aG1XMHRyP0Us6axAgQIBAPwX6WED0c9iWTYAAAQIECKxHQAGxHj3PJUCAAAECQyqggBjSxBs2AQIECBBYj4ACYj16nruxAvMPxt63XtF1MqUTKDeW2asRIEBgIwS2b8SLeA0CGyLQPInyew/E+Ki6dkM8vQgBAgQ2UcCWehNxvTQBAgQIEBhUAQXEoGbWuAgQIECAwCYKKCA2EddLEyBAgACBQRVQQAxqZo2LAAECBAhsooACYhNxvTQBAgQIEBhUgZGqeR3p9k/zuyg6mkt3D9VfBtH6GKV5YF0obcW37paVMfkqP1/2QJSVQ9ESIECAAIEsBBQQWaRBEAQIECBAoCwBBURZ+RItAQIECBDIQkABkUUaBEGAAAECBMoSUECUlS/REiBAgACBLAQUEFmkQRAECBAgQKAsAQVEWfkSLQECBAgQyEJAAZFFGgRBgAABAgTKElBAlJUv0RIgQIAAgSwEFBBZpEEQBAgQIECgLIGuS1mXFb5oCRAgQIAAga0QSL/iYHu60LRD+vigt12f3XdhNOe4eVDemi5nZeVMvsrLVxqxQxipiDYBAgQIECBQK6CAqCXSgQABAgQIEEgFFBCpiDYBAgQIECBQK6CAqCXSgQABAgQIEEgFFBCpiDYBAgQIECBQK6CAqCXSgQABAgQIEEgFFBCpiDYBAgQIECBQK6CAqCXSgQABAgQIEEgFFBCpiDYBAgQIECBQK6CAqCXSgQABAgQIEEgF+lhALMbCzIEYGxlpXTa4eVnT3r+7Y3LmdBr3ALVX4TB2IGYWFgdozJ1DWcX4W3Nj0OdBp4nbBAgQyF+gjwXEthgdn4q5qorm929U1fk4M70/GrErJqZPte9r3j8bB8evyV9y3RGm415yqaKam4rx0T6mat1jW+kFzIOVdDxGgACBXAUG9V0pV29xESBAgACBgRBQQAxEGg2CAAECBAhsrYACYmu9LY0AAQIECAyEgAIimzSeiIf27ug+kXSgT6DMBl8gBAgQIHCZAgqIywTbvO7LnEQ50CdQbp6mVyZAgACBzRVQQGyur1cnQIAAAQIDKaCAGMi0GhQBAgQIENhcAQXE5vp6dQIECBAgMJACCoiBTKtBESBAgACBzRVQQGyur1cnQIAAAQIDKTBSNa8j3f5pfhdFR3Pp7qH6yyBaHyU1D6wLpa341t2yMiZf5efLHoiycihaAgQIECCQhYACIos0CIIAAQIECJQloIAoK1+iJUCAAAECWQgoILJIgyAIECBAgEBZAgqIsvIlWgIECBAgkIWAAiKLNAiCAAECBAiUJaCAKCtfoiVAgAABAlkIKCCySIMgCBAgQIBAWQIKiLLyJVoCBAgQIJCFQNeVKLOIShAECBAgQIBAVgLpFYq3p9GlHdLHB73t8qouZd2c4+ZBeWu6nJWVM/kqL19pxA5hpCLaBAgQIECAQK2AAqKWSAcCBAgQIEAgFVBApCLaBAgQIECAQK2AAqKWSAcCBAgQIEAgFVBApCLaBAgQIECAQK2AAqKWSAcCBAgQIEAgFVBApCLaBAgQIECAQK2AAqKWSAcCBAgQIEAgFVBApCLaBAgQIECAQK2AAqKWSAcCBAgQIEAgFehjAbEYCzMHYmxkpHXZ4OZlTXv/7o7JmdNp3APUXoXD2IGYWVgcoDGnQzkdM5O7l8n/hXkxNjkTC+nTtAkQINA3gVVsu1vva4P7HtbHAmJbjI5PxVxVRfP7N6rqfJyZ3h+N2BUT06fa9zXvn42D49f0bYps3YLTcS+5VFHNTcX4aB9TtVUIjf0xfeZ8R+7fNJg7OB6jWxWH5RAgQKBWwHvYELwr1c4CHQgQIECAAIHLFFBAXCaY7gQIECBAgECEAsIsIECAAAECBC5bQAFx2WSb9YQT8dDeHd0nEg78CZQdnvMPxt63XtFl4ATKDiM3CRAgkImAAiKTRETXyaPtEwiH5QTKZh6WOYnSCZTZTFKBECBA4KKAAuIihRsECBAgQIDAagUUEKuV0o8AAQIECBC4KKCAuEjhBgECBAgQILBaAQXEaqX0I0CAAAECBC4KKCAuUrhBgAABAgQIrFZgpGpeR7r90/wuio7m0t1D9ZdBtD5GaR5YF0pb8a27ZWVMvsrPlz0QZeVQtAQIECBAIAsBBUQWaRAEAQIECBAoS0ABUVa+REuAAAECBLIQUEBkkQZBECBAgACBsgQUEGXlS7QECBAgQCALAQVEFmkQBAECBAgQKEtAAVFWvkRLgAABAgSyEFBAZJEGQRAgQIAAgbIEFBBl5Uu0BAgQIEAgCwEFRBZpEAQBAgQIEChLoOtS1mWFL1oCBAgQIEBgKwTSrzjYni407ZA+Puht12f3XRjNOW4elLemy1lZOZOv8vKVRuwQRiqiTYAAAQIECNQKKCBqiXQgQIAAAQIEUgEFRCqiTYAAAQIECNQKKCBqiXQgQIAAAQIEUgEFRCqiTYAAAQIECNQKKCBqiXQgQIAAAQIEUgEFRCqiTYAAAQIECNQKKCBqiXQgQIAAAQIEUgEFRCqiTYAAAQIECNQKKCBqiXQgQIAAAQIEUoE+FxCLsTBzIMZGRlqXDm5e2rTrd+xAzCwspnEPSHsV42+Z7I7JmdMDMuZ0GAxSEW0CBAiUINDnAmKJaFdMTJ+K5vdwdP3OTcX4aCZhLoW7YX+3xej4VMxdHPf5ODO9PxqReszGwfFrNmypeb0Qg7zyIRoCBAisTmBQ35lXN3q9CBAgQIAAgTUJKCDWxOZJBAgQIEBguAUUEMOdf6MnQIAAAQJrEsikgDgRD+3dMWQnUK4pX55EgAABAgSyEMikgEhPGmyfTDnQJ1BmkX9BECBAgACBNQlkUkCsKXZPIkCAAAECBPokoIDoE7zFEiBAgACBkgUUECVnT+wECBAgQKBPAgqIPsFbLAECBAgQKFlAAVFy9sROgAABAgT6JDBSNa8d3f5pfg9FR3Pp7qH6yyBaH6c1D6wLpa341t2yMiZf5efLHoiycihaAgQIECCQhYACIos0CIIAAQIECJQloIAoK1+iJUCAAAECWQgoILJIgyAIECBAgEBZAgqIsvIlWgIECBAgkIWAAiKLNAiCAAECBAiUJaCAKCtfoiVAgAABAlkIKCCySIMgCBAgQIBAWQIKiLLyJVoCBAgQIJCFgAIiizQIggABAgQIlCXQdSnrssIXLQECBAgQILAVAulXHGxPF5p2SB8f9Lbrs/sujOYcNw/KW9PlrKycyVd5+UojdggjFdEmQIAAAQIEagUUELVEOhAgQIAAAQKpgAIiFdEmQIAAAQIEagUUELVEOhAgQIAAAQKpgAIiFdEmQIAAAQIEagUUELVEOhAgQIAAAQKpgAIiFdEmQIAAAQIEagUUELVEOhAgQIAAAQKpgAIiFdEmQIAAAQIEagUUELVEOhAgQIAAAQKpQJ8LiMVYmDkQYyMjrUsHNy9t2vU7diBmFhbTuAekvYrxt0x2x+TM6QEZc69hnI6Zyd3due+YD2OTM7HQ66nuI0CAAIG+CPS5gFga866YmD4Vze/h6Pqdm4rx0UzCXAp3w/5ui9HxqZi7OO7zcWZ6fzQi9ZiNg+PXbNhSs32hxv6YPnO+ew5UVcwdHI/RbAMXGAECBIZPYFDfmYcvk0ZMgAABAgS2UEABsYXYFkWAAAECBAZFQAExKJk0DgIECBAgsIUCmRQQJ+KhvTu6T6Ib6BMotzDLpSxq/sHY+9YruuaBEyhLSaA4CRAYJoFMCoj0pMH2yZQDfQLlME2zVY51mZMonUC5Sj/dCBAgsIUCmRQQWzhiiyJAgAABAgTWLaCAWDehFyBAgAABAsMnoIAYvpwbMQECBAgQWLeAAmLdhF6AAAECBAgMn4ACYvhybsQECBAgQGDdAiNV89rR7Z/m91B0NJfuHqq/DKL1MUrzwLpQ2opv3S0rY/JVfr7sgSgrh6IlQIAAAQJZCCggskiDIAgQIECAQFkCCoiy8iVaAgQIECCQhYACIos0CIIAAQIECJQloIAoK1+iJUCAAAECWQgoILJIgyAIECBAgEBZAgqIsvIlWgIECBAgkIWAAiKLNAiCAAECBAiUJaCAKCtfoiVAgAABAlkIdF2JMouoBEGAAAECBAhkJZBeoXh7Gl3aIX180Nsur+pS1s05bh6Ut6bLWVk5k6/y8pVG7BBGKqJNgAABAgQI1AooIGqJdCBAgAABAgRSAQVEKqJNgAABAgQI1AooIGqJdCBAgAABAgRSAQVEKqJNgAABAgQI1AooIGqJdCBAgAABAgRSAQVEKqJNgAABAgQI1AooIGqJdCBAgAABAgRSAQVEKqJNgAABAgQI1AooIGqJdCBAgAABAgRSgT4XEIuxMHMgxkZGWpcObl7atOt37EDMLCymcQ9Qe9gNVjH+1rzYHZMzpwco74ZCgACBsgX6XEAs4e2KielT0fwejq7fuakYH80kzKVwN+XvsBpsi9HxqZi7mPvzcWZ6fzQi9ZiNg+PXbIq8FyVAgACByxcYhnfmy1fxDAIECBAgQGBFAQXEijweJECAAAECBHoJKCB6qbiPAAECBAgQWFEgkwLiRDy0d8cQnkDZmRsGnRpuEyBAgEDeApkUEOkJc+2TKYfmBMrmJGGQ96oiOgIECBDoFMikgOgMyW0CBAgQIEAgdwEFRO4ZEh8BAgQIEMhQQAGRYVKERIAAAQIEchdQQOSeIfERIECAAIEMBRQQGSZFSAQIECBAIHeBkap57ej2T/N7KDqaS3cP1V8G0fo4rXlgXShtxbfulpUx+So/X/ZAlJVD0RIgQIAAgSwEFBBZpEEQBAgQIECgLAEFRFn5Ei0BAgQIEMhCQAGRRRoEQYAAAQIEyhJQQJSVL9ESIECAAIEsBBQQWaRBEAQIECBAoCwBBURZ+RItAQIECBDIQkABkUUaBEGAAAECBMoSUECUlS/REiBAgACBLAQUEFmkQRAECBAgQKAsga5LWZcVvmgJECBAgACBrRBIv+Jge7rQtEP6+KC3XZ/dd2E057h5UN6aLmdl5Uy+ystXGrFDGKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAUUEKmINgECBAgQIFAroICoJdKBAAECBAgQSAX6XEAsxsLMgRgbGWldOrh5adOu37EDMbOwmMY9QG0GEadjZnJ3d+475sPY5EwsDFDWDYUAAQKlC/S5gFji2xUT06ei+T0cXb9zUzE+mkmYS+Fuyl8G0dgf02fOd8+Bqoq5g+MxuinuXpQAAQIE1iIwDO/Ma3HxHAIECBAgQGAFAQXECjgeIkCAAAECBHoLKCB6u7iXAAECBAgQWEEgkwLiRDy0d0f3SXQDfwJlZ2YYxPyDsfetV3TNAydQds4TtwkQIJCHQCYFxDInEA7NCZTNycBguZMonUCZx8ZCFAQIEOgUyKSA6AzJbQIECBAgQCB3AQVE7hkSHwECBAgQyFBAAZFhUoREgAABAgRyF1BA5J4h8REgQIAAgQwFFBAZJkVIBAgQIEAgd4GRqnnt6PZP83soOppLdw/VXwbR+hileQDs02QAAADwSURBVGBdKG3Ft+6WlTH5Kj9f9kCUlUPREiBAgACBLAQUEFmkQRAECBAgQKAsAQVEWfkSLQECBAgQyEJAAZFFGgRBgAABAgTKElBAlJUv0RIgQIAAgSwEFBBZpEEQBAgQIECgLAEFRFn5Ei0BAgQIEMhCQAGRRRoEQYAAAQIEyhJQQJSVL9ESIECAAIEsBBQQWaRBEAQIECBAoCyBrktZlxW+aAkQIECAAIGtEEi/4mB750LTBzsfc5sAAQIECBAgsCTgEMaShL8ECBAgQIDAqgUUEKum0pEAAQIECBBYElBALEn4S4AAAQIECKxa4P8DLMuRnLq848QAAAAASUVORK5CYII="></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State why the compound proposition \(\neg r \wedge (p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q)\) is not a logical contradiction.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A row from the truth table from part (c) is given below.</p>
<p><img src="images/Schermafbeelding_2017-08-17_om_06.50.05.png" alt="M17/5/MATSD/SP2/ENG/TZ2/02.e"></p>
<p>Write down <strong>one </strong>value of \(x\) that satisfies these truth values.</p>
<div class="marks">[1]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(p \Rightarrow (r \vee \neg q)\) <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for “\(p \Rightarrow \)”.</p>
<p>Award <strong><em>(A1) </em></strong>for “\(r \vee \neg q\)” or “\(r \vee q\)” (or “\(\neg q \vee r\)”or “\(q \vee r\)”)</p>
<p>Award <strong><em>(A1) </em></strong>for “\(\neg q\)”.</p>
<p>Award at most <strong><em>(A1)(A1)(A0) </em></strong>if parentheses are missing for \(r \vee \neg q\).</p>
<p>Award <strong><em>(A0)(A0)(A1) </em></strong>for \((p \Rightarrow r) \vee \neg q\).</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(x\) is not a multiple of 5 and (\(x\)) is (either) a factor of 60 or (\(x\)) is a multiple of 4, but not both <strong><em>(A1)(A1)(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for “\(x\) is not a multiple of 5”, <strong><em>(A1) </em></strong>for “(\(x\)) is a factor of 60 or (\(x\)) is a multiple of 4 but not both”, <strong><em>(A1) </em></strong>for “and” in the correct position. Accept only “<strong>but not both</strong>” in the second <strong><em>(A1)</em></strong>.</p>
<p>Award at most <strong><em>(A1)(A1)(A0) </em></strong>for using extra statements such as “If ...then”, “if and only if” etc.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-08-17_om_06.42.22.png" alt="M17/5/MATSD/SP2/ENG/TZ2/02.c/M"> <strong><em>(A1)(A1)(A1)</em>(ft)</strong></p>
<p> </p>
<p>Note: Award <strong><em>(A1) </em></strong>for each correct column. Last column follows through from previous two.</p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>because not all the entries in the \(\neg r \wedge (p\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{ \vee } q)\) column are F <strong><em>(R1)</em>(ft)</strong></p>
<p> </p>
<p><strong>Note:</strong> If all entries in the last column of their truth table are T, award <strong><em>(R1)</em>(ft) </strong>for an answer of “it is a tautology”. Only award <strong><em>(R1)</em>(ft) </strong>if the column is identified in the justification.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>accept one of: 1\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)2\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)3\(\,\,\,\)<strong>OR</strong>\(\,\,\,\)6 <strong><em>(A1)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(A1) </em></strong>for any <strong>one </strong>of the above answers.</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Forty families were surveyed about the places they went to on the weekend.</span> <span style="font-size: medium; font-family: times new roman,times;">The places were the circus (<em>C</em>), the museum (<em>M</em>) and the park (<em>P</em>).</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">16 families went to the circus</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">22 families went to the museum</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">14 families went to the park</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">4 families went to all three places</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">7 families went to both the circus and the museum, but not the park</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">3 families went to both the circus and the park, but not the museum</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">1 family went to the park only</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to represent the given information using sets labelled <em>C</em>, <em>M</em> and <em>P</em>. Complete the diagram to include the number of families represented in each region.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of families who</span></p>
<p><span>(i) went to the circus only;</span></p>
<p><span>(ii) went to the museum and the park but not the circus;</span></p>
<p><span>(iii) did not go to any of the three places on the weekend.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A family is chosen at random from the group of 40 families. Find the</span> <span>probability that the family went to</span></p>
<p><span>(i) the circus;</span></p>
<p><span>(ii) two or more places;</span></p>
<p><span>(iii) the park or the circus, but not the museum;</span></p>
<p><span>(iv) the museum, given that they also went to the circus.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two families are chosen at random from the group of 40 families.</span></p>
<p><span>Find the probability that both families went to the circus.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUIAAAERCAIAAACB1TmSAAAczElEQVR4nO2dv4vjSL7A699wPNHB3G3QKNhgoSMnE2iTThbOQSOYYINlD2RojoUNTlzgu4ZFDw4OBKODxz1YCiY5eBoQy4HgaDDowQZNcY/HsGqcNGIwhmqaQdQLvtMaj9t221KpfkjfTzY97Xa5XJ+qb32rVEUEgiCWQ3QXAEGQthytMUEQxAA+sfL9fPZs/T+fzebv4b9W89npw09PZ/NVrXH7zgNBkDZsaiyEENV1NB6R0Xl0vfz0l+9v6NfPzulNtfP1CIKoZ6fGo2m63PzlOxZ9F7G7Pa9HEEQ9WzSuWDQmzyb0l83fra6jF9+ly+qTF6DGCKKbxxrfseiMkLONUVcIIZbpxcXmEI0aI4h2Hmt8m05P1jJbNdUy/e5FdF19+lPUGEG080jjZTodkW0T49t0+vLxEI0aI4h2ti44bZsYr65mLy4fDdGoMYLoZ1PjBX25viz8QLVML55tGaJRYwTRz6bGy/RiRE6m6e0nv7W6mp1+OZu/e/L1CIKo59HcePVzNHlOTqev5otKCCHuF3M6m5yczq5WB7weQRD1bNv+sWJpNK03Xo4msx9TttXhx69HEEQ92zRu8XoEQdSDGiOI9aDGCGI9qDGCWA9qjCDWgxorpSgKxhhjjK4Rx7Hv+77vB0FAPwV+uSgK3QWXDOccPlqWZeufNwzDrVWRJElfq0IKqHFXFEWRJAm0S8/zYPXOdV1opnEcP9Z1V5t2XRdeDv8MwzBJkrIsdX/Eg+Cc53lOKYXCO46z/ll26bqrKjZeHsdxlmW2VEV3oMYyAXWDIHAcx3Vd8A3aZfs/Xo9gG2+R5znnvP3fl0tRFKAuIcTzPEppnueMMSnK1VVBKa2rIo5jM6tCAaixBIqiCMPQcRzHcYIgUDY+bKiSZZn2RswYg6pQ3MWA0hD1wFeg4E3NATVuRZZlEOnFcaxx2sY5r0sShqGUwb9BATzPcxyHUqoxyjWnJCpBjZtQliWl1HEcQ8bAmrIs4zh2Xdd13SRJFBQM3tFxHN/3jRoDIS6AwVl9v6YY1Pg4yrKExqFl0DucPM9h0tjdiMQYg7cIw9DYBDLnnFIK/ZpRvYxcUONDYYzV8bMtodp6pyOxzHVVUErNiUT2k2VZLbMtZT4c1Php8jy3rtWuI1HmWgY1Ebt0bOyADgE13gd86/2Ix0Dmxi2YMdab0HRdZt1lkYNFGi9ZSqPp+OH+memr+c1y/tfZxkElkijLsp5bdvH3dVEUBbTgw21s8BIrqPvoPM9Vvef7BX35oQGPI1Y9+v/qLT1//uEXJnRx8N+1QuNqxf57NnlORpMZ/XAoSbXILifPCXlJF4+O+WsHJEUIIXEc9ynuWqceWvdn6TjnbQZwK4Bpgu/76hKWy3Q6ImR0sXFzA1yuNCJk271LT2C+xtXq+tVkRMjp9+ni/pP/YNF4a5fWgjzPYe3EliRWG7Isg/0qWxVNkgSy0L2vCui4IXmpoLd6uO1w80aH6oaejwghW4+XfgLjNV5dzU5HZPQ1vbnf/K8Fffn4VPwWwPqnwhBLP5zzIAg2huWtP+w9nHPY/d7x4tkdi86/mnw52jh/tnpLz0+/mnw52nq89FMYrjHcRDPadaCfLIqi8DzP87zejzxbgYEXsgBFUbiuu2uI7j0wLHeZBfiFTr75L/qHT0+Dh7tK//bmrzvuXXoKszWGK1obfbDDgdiyZ6msY4GO7OzsjBCSJInu4ugEEgdddWTLdPoiYjd08vHu8Gp1/Woyvpyv3tLJs233Lj2N2Rov6OSTq9LlAymcQUWPW+Gcf/vtt59//vlnn31m7JYsZdTTCulV8X4+O5nN38P8GHLR9SHwO+9dehqjNf6QDDgm834UYRh6njfM6HEdzjnMKeC5Asdx0GTx0MVLrYo7Fr2cprdC/PIw8L6bz76EOePOe5cOwGiNOx2N0WFg3WH4CZpcI9vkX+jkG7p4L8RqPjsl5Dyifzw9vZyvqn0XEh+A2Rp/WA1/fk7ffrqudL9IZxebPzwCdBh47DCAJtfINBkmxpVY2wfy4sOdSpAGajpima3xx8W08fTVFWz8ECuWRheTizeLphKjw8AuhwE0uUaSycvr6Pz5Q1prmV6MPo5P94v0+9MW80fTNRZCVIv564Mvo3kSdBjY7zCAJte0rIqHLR8ft2FWLHpxTm+qh01dH2myMdECjSWCDgOHOAygyTUmV8WANEaHgcMdBkxuvooxtiqGojE6DBzrMGBs81WPmVUxCI3RYaCZw4CZzVcLBlZF/zWO4xgdBlp2Z9B8h7ntfIMkSVzXNadR9VxjePAQW554kLBly4M+UVaRrCYIgiAIdJfiA33WmHM+tAcPd1EUhayt457nxXHc/u/YDuccziTTXRAh+q0xXHekuxT6gSmxrEe4yrLEh0mAoigIISZMknurMVwFYs7sRSNwY6PEPyglPu8HhjSzfmrMGDMtl6gLyA5Ib2dwxaHcv2kpcLGj3jL0U2PP8wyZtOgF5m9dZAe6+8vWASkYvbOMHmoMZx3qLoURwH2LHf1xrOeaTuv5EPqmsQldoyEoqAqMemr0HsTfN42194vmEIZh14l6yEFoT/CYgN7YpFcaw1oIZrbEw0Kxgn0vQRBoT/AYgu/7ug5m7JXGCsYfW1DWpMqyJITgPjmhNTbpj8bYnmoUtyfsPWvCMNQyIPdHY2xMNYqjO+xAa2Bap35A7onG2JJqtIR22IfWaBmQe6IxNqMaLYkW7EZrILmouBvtg8bYhmo0ZlmwJ61R35P2QWNsQDUa1zywM61R35larzHnHFsPoCu/UhOGIa4hA77vq9zUZb3GWZbhti0gjmO9UQlMCzUWwByyLFN5TIr1Gnuep3Evq1GYsIMNH3uqUfl12K0xdv81eZ6b8LxRkiTmnFClF5XBkd0a42SsJggCEx42wlRFjcpUhcUaw4N42GLEQ5bYkCeNdG1INBBliS6LNVacRTCZJEnMWXLL8xy/F0BZ/tVijeM4NqzXX7I3lxO4He90+mre+ObWo2kRUd+m0xOywRju4G1O96EBXCwqrcAdAVGSgjeyWGPP80w65eP+5vV/XL5hKyFEtbi6nIzqG6i7x3XdhknRzVs5CSGjcXTdUgrf97vNV3+4v15agbuj+VdzDBZrbM5sUAghqv/76adfPjam6joaj0bTdNn9O7fo8qtl+sN36c2aA7fp9GXE7loWqeNAqVrNL8dK6rY9alKPtmrMGDN7AnabTk/UaJznedMJ2P2CvV2/8L1i0VhGgNqiSIcAE4HxNKIpM91lNWkLWzWmlJqT1NnGbTodn9O3CoI9eUPfHYvOpZS50zlhxaLx2jx+Sq9XT79IG4wxBev5tmocBIHRm7eW6XR8OV+pmLJJm4hW19GL79KlnDJ3PSesFvPX0fSUEKIwB9EMBbM/WzVWkzloyrv57BtlbUtWK6lY9ELeLEDNnLBavLk4VZSDaIzv+13nYm3VWPte7t1Uq/lfptHPaiI92Cok4y/dsejlNL2V8aeEEIJSqmQ5sFqmF6PRhawgogvCMOy6R7NSYzXzjWZUN/+4fKXIYSEEY0xOMklqRC06z3J9RFZarjsopV1vGbZSY2VN5FiqRXp5mT5s+6hW1z9GP0kb37YiK9UnN6IWQhRFoaSrrZbpHy/kBRFdIK2r3Y2VGqsK2I6iWjE6Pd3YS3HWfg12P5LS1JIjaqCbtnG/mP/j9YcdcveLq79Mv3ujbrtcIxQ8h2elxgamqasber65HUrFJkE56ZPqOjr/QXpevZs05P0i/f4Udm9NZj+mzOTVppquNbFSYwWpP1sw+Rmvzrdk2kPXG4et1NisbZhaMThjb+bcRw9dDzy2aqz+Tc3E5KpAjWu6ngaixhZj+BlGqHFN11WBGluMgpWMNqDGNajxJvL2LVmP4Robu7yvHtR4E8PbrkoMrwrDi6cS1HgTbBw1hleF4cVTSddPHaPGFqNgs24b8Juq6boqUGOLMXzyid9UTZZlnZ7CjxpbjOFVYXjxVIJz401UPTpjAYZ7YnjxVIIam/KmBtLek7Is2W5aFs/wqbtKUGNT3tRADg9MQFd4ONn3/foRLMdx/B14nlf/muu6cAF6kiSMsQM3tOP2jxrU2JQ3NZM9VVEUBaUUbARd4zgGD499KKooijzP13sBx3HgtK09fwo1rsE91dvfFJ9wAjbqvyxLSIo6juO6bhzHeZ53UVdb32jjd1DjGnzCaQuGXfuiE3jeuCzLJElg4H1ykJQOYyyO4/rdsyyDjgOfN67B5423YODpH1ooy/Ls7Ozs7MxxnDAMtTuz0Zt88cUX//73v/UWyRDw9I8tYLQGl8I6jvPb3/72T3/6k+7ibAI+Q3osDEODTxRXAZ7FtR3Ddy91SpZlruu6rgvxiLGX4EAWvSxLSikk2AY7D8KTMbdj8jnVHcE5r31YD56N3WKx3tXuKvxAwHOqjXtfLewZ0Ix9+vrxxIdzDqGE53mDCrPx1oidmH2HkzTg/tf9eU4zl9/23OGUJInjOMPJbuAdTjvpfbKacx7H8SHN3cxpp+u6e0pVliVsFDOw5NJR0M/aqnG/9+vmeQ7bpA5Z/pV3v7E0OOeHNAwYluM4NjCakIWaJ3ls1RiiTS1v3Smc8zAMHcc5PBWUZZlpWa7DE2/1sNzXKVKSJJ0+aQzYqvGB/b1dFEXheZ7v+0eNTgYec3tsrAQ5PAX3IasnDEMFsZKtGounZl/WAYF0s5mCaVfA+L5/bOYCFhGDIOhZgK1m/m+xxgry+MqAbFbjNVXT1mObdSuc8yAIetY7qxHEYo27Pm1QDdB2W04OjUr4tVzKhrxXP5Yh8jxXk8GxWGNoLlbHYJxzz/PaR5KMMQnT4+otPT8ZR9ct70eN47hl9wqz/R700WomxsJqjYUQvu/bG1fLbaye57Ubwe5v6NcjMmqvseM47dPOZVlK6eA0AllYNTkLuzXO89zSzdWQ0JIYOrZbdqpW8x8mv/vdZNRWY3j0qsUf+AjnHNaiLDWZUqpgqQmwW2MhhOu6RmV3DiHLMunTP85583z16mo2+WF+82baWuMGOer9wCq6javKKnN11musZnldIjAOd9EuwzBsFKK/m8++mc3fiWXaUmOYJkgfPOM4dl3XrjFZcZxovcYqZyDtgYbeURq2Uc6vWs1/mMyuVkK01zgMw44S5mEY2hVdK87aWK+x6LL1yAXi3k6/3aNbz+rq8uL1DYjbTuNWUf0BeJ5nS+5a/RpKHzS2YuUJ1pa6bohHHqjwbn75R3pz/+Ff7TTu+hwSqEAr+mv140ofNBZCBEFg2lM+GwRBoOYBhiNWnpbpdES2cRaxu6PeFIbirjM6nU5JZFGWpfpZXk80hv0Pxg7IcOy7muLBCRtNXtliNKaUqumkwGSTE9dNE42t6InGooOlDlkURUEIUdny6gP3jqOFxgqG4hqVfeKxdJ0g2EV/NDbznD3Oueu6ireaNdwK0lRj9Q88+75vZrpL5ZaPdfqjsWg8CnVJEARavleVew/UVzsMeqZt+1GTINhKrzQ2bYacJImufQvNZ8hHomxWvAHsojFqv0Acx7p2IvVKYyEE3N+puxRC6JgSb+B5XtfBvMbxRwgRx7E5pxdpSVDX9E1jvbW5jud5ejsUBbGJlqzsOtoruQbundX17n3TWBjQtsRDNlVvGUTHbQvCDb09pvaQB9A+m+uhxnojPdGubVWL7HLynBBCTi8oW7YsSaexydHzl2oxf/2fs8lzQk6m6a2sYpjQYyqYv+ynhxoL3UuLzSO91f/QV/9aVEJUi6vLyWh0kS5bPsMv4Obhln/kMfCs5eE1DN3TaDL7MWUr2YXRG1qb0I/0U2Ohb2mxxZd6978//eum1naZTkcSRq0utiLDVqoj4p3V1ez0ZHKZLdp2SjvLoyu0hnBae1TfW4217LuAeF7Kl1qxaHx6OV9JaPjw6Iispd3jK/bdfPZidE5vunEY0LLuJbdi29BbjUWDQaM1kjbxLFkaTSd/SBf3T//uYUgcNHzfP+ozViwak/E0+tts8pwQMppcvmk953+M+l2QRj1x1WeNxcMUTs23Kye19vGpo/GUXkucRkrZi3J80uGORWfkdPpqvqiEEKufo8lzIinKeFw2ldOoMAzNWbXuucZC4cEREuO6anH1ajom5Pk5fSuxvcOB2I1fDn3ikUP6bTo9GU3TevytWDSWcf7mY1RuGTg2w9c1/ddYqDJZcgBfXUfj0boA7WlzdEGe54SQoz/g40/RweeqUbNloFF31i2D0FjByRsdPOVzx6Iz6c29WVW0eF7/Np2ekHHE6sG3uo7Gz7oYjcXDgNxpf22gw2IgGovuTe7gnN3bdDqWG1QDx1ZFuzM3qmV6MRp9/elRQUefLnI4nd7sxRhrEpJ0z1A0Fl2aLOdq0uotPT85nf5tvrgX4n6Rfj+evLruIBUkHlZKDmnuEs7Nqd7S8+cj+CzV4uryfAwHcXZDd9cmmXyE0IA0Fg/JZOkmt7+1SAghxPI6Ov+QpR5NZnTe0WYJ4JBGCb8jYXBbsTezyQjS76+uOv1coptrYk12WAxNYyFEURSu68o12cabK8RD09y18gn/a8jzQ0chPa6GVXdjHRYD1FjIjq7lRNSa2NWpGT747EduXJ1lGSHE8KoYosbiwWQpq1CSImptPO7UrGi4+5EVV0Ne2sCc1gYD1Vis3Q/e0mRLI+p1wGTf9znn0HBt/0RS4mpKqYFrS1sZrsYAXNjXuLu1OqJeh3P+7bfffv7555999pkVDXc/LeNq6OJd17WlKoausXgInJrlcpIksTqirimKwvM813UJIfbe/L5O430gcFKyXTeko8ZCPDRi3/ePnVAFQWD1HBJY78gg6WVXI95Ks+sHIJC2riNDjT8Sx/Gx08Kut/51DUSPG9OKOqQ0P7Wzh2MDJc657/ue59kSSK+DGn8CnH584FjU3YYhNcBV2rs+bJIksKpsaT91VNrC9g+LGm/COYe815ORVRzHhjw1fixlWfq+/2ToceCvGcshOaqiKHzftz30QI23A3kO3/f3tANLv3uY/h0+8sCg3SBxoJ0wDPdkLjnnlFJCiI071TZAjfdRf81bW7x1n50xBpteju19OOeQONhVFWaSZdmu84bgchwb+6atoMZPUJYlJIHiOF7/ys28wHEXjDEIj9uMPBB/WiQzdFsbPwSBDby1rw2o8UGUZRmGISEkDEOQOc9zc45i2sO6wFLcY4xB7qCuCpOp2yfnHE4j65nAAGp8BCAztOA///nPhs+poKPpaPBc79dMXqFxHOfnn3+GdIDv+zbmMg4BNT4aSI386le/+uKLL+I4Nq0R53kOfQ3cSNJp9FuWZRzHMMSZVhUw/P7mN7/59a9/HYZhXwUGUOOGeJ73z3/+ExI/rutSSjU2Ys75hr2Kw129774OPN0RBAEhJAiC3//+93//+991FUYZqHFD1j943Ygh3s6yTE07LooCTtUlhGj3B6irAh5jzvNcTTKMMQZnaBNCfN+vw5DebHrfD2rckK0fvCiKJEkgsw3tOMsyieEc55wxBqONelWOYsMrSiljTGIvA1WxXttxHD+uCsjwyXpTY0GNm8A5f/KDw1AJjzQTQiDFEsdxkiTsgV36lWVZ/w6lNI5jSFaBEkEQJEli1ER0DxDwr38Ez/OCIKCU5nlef8xdLy+KYr0q4K6GuirgueI9vQNq3OT1A6FB44DmWDdEgOwAnAfiOJY+lGmkDihgOgBAT7cV2KRRVwV0godXBWrc5PUDYSCNowcM5JtCjZswkMbRAw6Z/vQA1LgJqLFFDKGJosZNsGUnJiKG0URR4yZA9lh3KZCDGEITRY2bgEG1RQyhiaLGTUCNLWIITRQ1bgJqbAtwd6TuUnQOatwE1NgWBvJNocZNgMOcdZcCeRrUuMnrh8NgP7hdoMZNXj8cBvvB7WIgK/yocUNsuWtv4FBKDT9rSQqocUN6fLBTn+jHJVtPgho3BJ4f1F0K5AkaHMptI6hxQwZyOoztDKR9osYNGUgK1Gp6c4n8k6DGDRnIg6xWM5yuFjVujuM4vThYp1qxn+iPs8mzi3RZ6S6MTIbzIBpq3Jx+ZEErFr34avLViJBR3zT2PM/SK12PBTVuDpyuqrsUUrhj0VnPNIZZj4FH/3YBatycHj0900ONB7J/C0CNW2HpTeWP6KHG++8o7xmocSviOO5FEqWHGruuO5zdsqhxK/I8f3wRtoX0TePhrBgDqHFbCCH2Lzv1TeOh7bFDjdsCNyrpLkVL+qbxcJaaANS4LVmW2R9X90rjHq0gHApq3BZYn7Q8ru6VxkOLqAVqLAW74+plOh3VFxiOxtG17SoPLaIWqLEUehFX94QBRtQCNZZCL+LqngA3SOsuhWpQYzmEYTjA1mMgfdlXdxyosRwglhvIRnxjybJsOPuo10GNpTGoTbxm4rpuDx4dbQBqLA3GGA7IGsmybLBXeaDGMvF9HwdkXfi+P8yhWKDGcoEBWXcphsjAax41lgwOyFrwPG/I1Y4aS6YoClxDVgyldODbb1Bj+VBKh7nsoQVY6hvgWvE6qLF8OOeDXflQj+/7vTiApRWocSfg4pMa8jx3XRfrGTXuiiAIcHtmp3DOHccZ2sNMW0GNuwIaGYbW3REEQV/OCW8LatwhEFoP53xGlUB2GsNpADXuliRJcPImnTzPsX9cBzXunDAMcf1JIrDChFPidVDjzuGce56HiyJSwMrcCmqsAhhAMN3VHgxttoIaKwI2aeJ0rg1xHGNaayuosTqyLMPETGOg9nCz+lZQY6XgMkkzcOluP6ixasIwHPjjOMcC96phZmEPqLEGPM8LggDH5EMAhy0+zV8JqLEGOOdBEGB0/SSwzQPH4SdBjbURhiHO9/YAOS3c5nEIqLFOkiTBlroV7OOOAjXWDIw5OPer4Zz7vo8zjqNAjfUDWZwwDLHhMsZc18X837GgxkZQD0FD3t5AKcXApBmosUHEcTzMqXLdi+FkuBmosVnAEsugjlyGHVo4p2gDamwcRVF4nud5Xu8PbYX182EGIHJBjQ0F1qLiOO7rGAVxB2azpIAam0tZlr0crHAQlg5qbDpwFLPv+z2IsTnnsE6Og7BcUGML4JzDYoy9d3+uf4Qe9EemgRrbBNzEbdfNMmVZosBdgxrbR5Zlnue5rhvHsckLrXmeh2FICAnDcMjbWhSAGttKURRxHMPgbJTPYK/jOJ7nJUmCAisANbaeDZ+1BK6Qu0J7dYEa9wfw2fM8QkgQBApcYozB6WKEEN/30V5doMY9pCzLLMtgbdZ13TAMKaWMsfaBN2MsyzJKaf3H4zjO8xxXj/SCGvccxliSJHEc+77vOA4hBE4Cow8kScIeAa4C8FrXdeG1vu9TSrMsw4HXHFDjwbFhKdzD8Bi6Rp7n5qTQkMegxghiPagxglgPaowg1oMaI4j1oMYIYj2oMYJYD2qMINaDGiOI9aDGCGI9qDGCWA9qjCDWgxojiPWgxghiPagxglgPaowg1oMaI7/QyTOywWgyo/NFpbtoyGGgxogQ4jadnhByOpuvhBCiWlxdTkZkdDq7WukuGXIIqDEiPmg8ukiXD+Pv+/nsGfnkJ4jBoMbIB2lH03RZ/2SZTkeosTWgxoioWDQmo3F0/aDs/Q39ekQ+FRsxGNQYuWPRGSEn0/RWCCGqxZzOJiNCTr9PF/e6y4YcBGqMwMT4q+nvxh/S1KfT6DWmqW0CNR48y3Q6wvjZblDjoQPprbWJMWIfqPHAgYnxWcTudJcEaQ5qPGiqG3o+IuTZbP5ed1GQFqDGg2U1n52ubb/EAdliUGMEsR7UGEGsBzVGEOtBjRHEelBjBLEeCRojCKKdVhojCGIa/w/U+7F3GYRjigAAAABJRU5ErkJggg==" alt><span> <em><strong>(A1)(A1)(A1)(A1)</strong></em></span></span></p>
<p><span>Award <em><strong>(A1)</strong></em> for 3 intersecting circles and rectangle, <em><strong>(A1)</strong></em> for 1, 3, 4 and 7, <em><strong>(A1)</strong></em> for 2, <em><strong>(A1)</strong></em> for 6 and 5.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) 2 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>(ii) 6 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>(iii) 40 − (1 + 6 + 2 + 3 + 4 + 7 + 5) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting all their values from 40.</span></p>
<p><br><span>= 12 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p> </p>
<p><span><strong>Note:</strong> Follow through from their Venn diagram for parts (i), (ii) and (iii).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{16}}{{40}}\left( {\frac{2}{5},0.4,40\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator. Answer must be less than 1 otherwise award <em><strong>(A0)(A0)</strong></em>. Award <em><strong>(A0)(A0)</strong></em> if answer is given as incorrect reduced fraction without working.</span></p>
<p><br><span>(ii) \(\frac{{20}}{{40}}\left( {\frac{1}{2},0.5,50\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft) <em>(A1) (G2)</em></strong></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for numerator, <em><strong>(A1)</strong></em> for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award <em><strong>(A0)(A0)</strong></em>. Award <em><strong>(A0)(A0)</strong></em> if answer is given as incorrect reduced fraction without working.</span></p>
<p><br><span>(iii) \(\frac{6}{{40}}\left( {\frac{3}{{20}},0.15,15\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for numerator, <em><strong>(A1)</strong></em> for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award <em><strong>(A0)(A0)</strong></em>. Award <em><strong>(A0)(A0)</strong></em> if answer is given as incorrect reduced fraction without working.</span></p>
<p><br><span>(iv) \(\frac{{11}}{{16}}\left( {0.6875,68.75\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for numerator, <em><strong>(A1)</strong></em> for denominator. Follow through from their Venn diagram. Answer must be less than 1 otherwise award <em><strong>(A0)(A0)</strong></em>. Award <em><strong>(A0)(A0)</strong></em> if answer is given as incorrect reduced fraction without working.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{16}}{{40}} \times \frac{{15}}{{39}}\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for multiplication of their probabilities, <em><strong>(A1)</strong></em><strong>(ft)</strong> for their correct probabilities.</span></p>
<p><br><span>\(\frac{{240}}{{1560}}\left( {\frac{2}{{13}},0.153846...,15.4\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their answer to part (c)(i). Answer must be less than 1 otherwise award at most <em><strong>(A1)(A1)(A0)</strong></em><strong>(ft)</strong>.</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">A group of tourists went on safari to a game reserve. The game warden wanted to know how many of the tourists saw Leopard (\(L\)), Cheetah (</span></span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">\(C\)) or Rhino (</span></span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="line-height: normal;">\(R\)). The results are given as follows.</span></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 5 of the tourists saw all three</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 7 saw Leopard and Rhino</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 1 saw Cheetah and Leopard <strong>but not </strong>Rhino</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 4 saw Leopard <strong>only</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 3 saw Cheetah <strong>only</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;"> 9 saw Rhino <strong>only</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to show this information.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 25 tourists in the group and every tourist saw at least one of the three types of animal.</span></p>
<p><span>Find the number of tourists that saw Cheetah and Rhino <strong>but not </strong>Leopard.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 25 tourists in the group and every tourist saw at least one of the three types of animal.</span></p>
<p><span>Calculate the probability that a tourist chosen at random from the group</span></p>
<p><span>(i) saw Leopard;</span></p>
<p><span>(ii) saw <strong>only one </strong>of the three types of animal;</span></p>
<p><span>(iii) saw <strong>only </strong>Leopard, given that he saw only one of the three types of animal.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 25 tourists in the group and every tourist saw at least one of the three types of animal.</span></p>
<p><span>If a tourist chosen at random from the group saw Leopard, find the probability that he also saw Cheetah.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="images/Schermafbeelding_2014-09-21_om_07.26.52.png" alt><span> <strong><em>(A1)(A1)(A1)(A1)</em></strong></span></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles (the rectangle need not be labelled), <strong><em>(A1) </em></strong>for 5, <strong><em>(A1) </em></strong>for 2 and 1,</span><span> </span><strong><em>(A1) </em></strong><span>for 4, 3 and 9.</span></p>
<p> </p>
<p><span><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(25 - (5 + 2 + 1 + 4 + 3 + 9)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(M1) </em></strong>for their \(5 + 2 + 1 + 4 + 3 + 9\) seen even if total is greater than \(25\).</span></p>
<p><span> Do not award <strong><em>(A1)</em>(ft) </strong>if their total is greater than \(25\).</span></p>
<p> </p>
<p><span>\( = 1\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{12}}{{25}}{\text{ }}(0.48,{\text{ }}48\% )\) <strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1) </em></strong>for denominator.</span></p>
<p><span> Follow through from Venn diagram.</span></p>
<p> </p>
<p><span>(ii) \(\frac{{16}}{{25}}{\text{ }}(0.64,{\text{ }}64\% )\) <strong><em>(A1)(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1) </em></strong>for denominator.</span></p>
<p><span> There is no follow through; all information is given.</span></p>
<p> </p>
<p><span>(iii) \(\frac{4}{{16}}{\text{ }}(0.25,{\text{ }}25\% )\)) <strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator.</span></p>
<p><span> Follow through from part (c)(ii) <strong>only</strong>.</span></p>
<p> </p>
<p><span><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{6}{{12}}{\text{ }}(0.5,{\text{ }}50\% )\) <strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator.</span></p>
<p><span> Follow through from Venn diagram.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider the following statements.</p>
<p class="p1"><span class="Apple-converted-space"> </span>\(p\): the land has been purchased</p>
<p class="p1"><span class="Apple-converted-space"> </span>\(q\): the building permit has been obtained</p>
<p class="p1"><span class="Apple-converted-space"> </span>\(r\): the land can be used for residential purposes</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write the following argument in symbolic form.</p>
<p class="p1">“If the land has been purchased and the building permit has been obtained, then the land can be used for residential purposes.”</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><strong>In your answer booklet</strong>, copy and complete a truth table for the argument in part (a).</p>
<p class="p1">Begin your truth table as follows.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-21_om_06.44.01.png" alt></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Use your truth table to determine whether the argument in part (a) is valid.</p>
<p class="p1">Give a reason for your decision.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the inverse of the argument in part (a)</p>
<p class="p1">(i) in symbolic form;</p>
<p class="p1">(ii) in words.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\((p \wedge q) \Rightarrow r\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for conjunction seen, award <strong><em>(A1) </em></strong>for implication seen, award <strong><em>(A1) </em></strong>for correct simple propositions in correct order (the parentheses <strong>are </strong>required). Accept \(r \Leftarrow (p \wedge q)\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1"><img src="images/Schermafbeelding_2015-12-21_om_06.49.11.png" alt> <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for each correct column, follow through to the final column from <strong>their</strong> \((p \wedge q)\) column. For the second <strong><em>(A1)</em>(ft) </strong>to be awarded there must be an implication in part (a).</p>
<p class="p1">Follow through from part (a).</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">The argument is not valid since not all entries in the final column are T. <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(R1)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Do not award <strong><em>(A1)</em>(ft)<em>(R0)</em></strong>. Follow through from part (b).</p>
<p class="p1">Accept “The argument is not valid since \((p \wedge q) \Rightarrow r\) is not a tautology”.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\neg (p \wedge q) \Rightarrow \neg r\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p class="p1"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\((\neg p \vee \neg q) \Rightarrow \neg r\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes:<span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for the negation of their antecedent and the negation of their consequent, <strong><em>(A1)</em>(ft) </strong>for their fully correct answer.</p>
<p class="p1">Follow through from part (a). Accept \(\neg r \Leftarrow \neg (p \wedge q)\) or \(\neg r \Leftarrow (\neg p \vee \neg q)\)<em>. </em>Follow through from part (a).</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>if it is <strong>not the case </strong>that the land has been purchased <strong>and </strong>the building permit has been obtained then the land can <strong>not </strong>be used for residential purposes. <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)</strong></p>
<p class="p1"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">if (either) the land has <strong>not </strong>been purchased <strong>or </strong>the building permit has <strong>not </strong>been obtained then the land can <strong>not </strong>be used for residential purposes. <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for “if… then…” seen, <strong><em>(A1)</em>(ft) </strong>for correct statements in correct order. Follow through from part (d)(i).</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Forming the statement in part (a) was attainable by the great majority, although the lack of parentheses was a common fault.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The truth table in part (b) saw less success and it was clear that some centres simply had not prepared their candidates in this area of the course.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Where the truth table was correctly constructed many candidates were not aware of the conditions required for an argument to be valid and in part (d) the converse and the inverse were often confused.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Where the truth table was correctly constructed many candidates were not aware of the conditions required for an argument to be valid and in part (d) the converse and the inverse were often confused.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman';"><span style="font-family: 'times new roman', times; font-size: medium;">A group of \(120\) women in the USA were asked whether they had visited the continents of Europe (\(E\)) or South America (\(S\)) or Asia (\(A\)).</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(7\) had visited all three continents</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(28\) had visited Europe only</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(22\) had visited South America only</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(16\) had visited Asia only</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(15\) had visited Europe and South America but had not visited Asia</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(x\) had visited South America and Asia but had not visited Europe</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(2x\) had visited Europe and Asia but had not visited South America</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> \(20\) had not visited any of these continents</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram, using sets labelled \(E\), \(S\) and \(A\), to show this information.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the value of<em> </em>\(x\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Explain, in words, the meaning of \((E \cup S) \cap A'\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n\left( {(E \cup S \cup A)'} \right)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a woman selected at random from the group had visited Europe.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a woman selected at random from the group had visited Europe, given that she had visited Asia.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two women from the group are selected at random.</span></p>
<p><span>Find the probability that both women selected had visited South America.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><span><img src="images/Schermafbeelding_2014-09-03_om_13.53.08.png" alt><span> </span></span><span><strong><em>(A1)(A1)(A1)(A1)(A1)</em></strong></span></span></p>
<p><span> </span></p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for \(7\) in correct place.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for \(28\), \(22\) and \(16\) in the correct places.</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for \(15\), \(x\) and \(2x\) in the correct places<em>.</em></span></p>
<p><span><em> </em>Award <strong><em>(A1) </em></strong>for \(20\) in the correct place.</span></p>
<p><span> Accept \(4\) and \(8\) instead of \(x\) and \(2x\).</span></p>
<p><span> Do not penalize if \(U\) is omitted from the diagram.</span></p>
<p><span> </span></p>
<p><span><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(3x = 120 - (20 + 28 + 15 + 22 + 7 + 16)\) <strong><em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for setting up a correct equation involving \(x\), the \(120\) and values from their diagram.</span></p>
<p> </p>
<p><span>\(x = 4\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Follow through from part (a). For the follow through to be awarded \(x\) must be a positive integer.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(Women who had visited) Europe <strong>or </strong>South America and (but had) <strong>not </strong>(visited) Asia <strong><em>(A1)(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for “(visited) Europe <strong>or </strong>South America” (or both).</span></p>
<p><span> Award <strong><em>(A1) </em></strong>for “and (but) had <strong>not </strong>visited Asia”.</span></p>
<p><span> \(E\)(urope) union \(S\)(outh America) intersected with not \(A\)(sia) earns no marks, <strong><em>(A0)</em></strong><em>.</em></span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(20\) <strong><em>(A1)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A0) </em></strong>for the embedded answer of \(n(20)\).</span></p>
<p> </p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{58}}{{120}}{\text{ }}\left( {\frac{{29}}{{60}},{\text{ 0.483, 48.3% }}} \right){\text{ (0.48333}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, follow through from their value of \(x\), or their diagram, <strong><em>(A1) </em></strong>for denominator.</span></p>
<p> </p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{15}}{{35}}{\text{ }}\left( {\frac{3}{7},{\text{ 0.429, 42.9% }}} \right){\text{ (0.428571}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator, follow through from their value of \(x\) or their diagram. </span></p>
<p><span><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{48}}{{120}} \times \frac{{47}}{{119}}\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)</em>(ft) </strong>for two correct fractions, follow through from their denominator in part (e), follow through the numerator from their answer to part (b) or from their diagram, <strong><em>(M1) </em></strong>for multiplication of their two fractions.</span></p>
<p> </p>
<p><span>\( = \frac{{2256}}{{14\,280}}\left( {\frac{{94}}{{595}},{\text{ 0.158, 15,8% }}} \right){\text{ (0.157983}} \ldots {\text{)}}\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p> </p>
<p><span><strong>Notes: </strong>Award <strong><em>(A1)(M1)(A1) </em></strong>for correct fractions, correctly multiplied together with an answer of \(0.16\).</span></p>
<p><span> Award <strong><em>(A0)(M1)(A0) </em></strong>for \(\frac{{48}}{{120}} \times \frac{{48}}{{120}} = 0.16\).</span></p>
<p><span> Award <strong><em>(G1) </em></strong>for an answer of \(0.16\) with no working seen.</span></p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates seemed to be well-drilled in the technique of creating Venn diagrams and using the data from their diagrams to solve problems in probability and this question was well answered. Except for the odd mistake in determining the value of <em>x</em> in part (b), many candidates scored full marks on the first two parts of the question. Indeed, those who calculated an incorrect value of <em>x</em> were able to recover many of the marks in the remainder of the question with the use of follow through marks. ‘Explain in words…’ required candidates to answer part (c) in the context of the question so ‘<em>E </em>union <em>S </em>intersection not <em>A</em>’ earned no marks. Of those candidates who did answer in context, many scored 1 mark for ‘had not visited Asia’ but a significant number used ‘and’ rather than ‘or’ and consequently were not awarded the other mark for expressing \(E \cup S\) in words. Whilst many correct answers of 20 were seen for part (d), a significant number of candidates wrote down the incorrect value of 113 which presumably was arrived at by evaluating \(n((E \cap S \cap A)')\) rather than the actual demand of the question. Having a Venn diagram seemed to be a good aid for parts (e) and (f) and much good work was seen in these two parts. However, in part (g), a significant number of candidates either chose a <span style="font: 19.0px Arial;">“</span>with replacement<span style="font: 19.0px Arial;">” </span>method or simply did not know what to do with the probabilities once they were found. As a consequence, this part of the question proved to be quite a discriminator.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A group of <span class="s1">66 </span>people went on holiday to Hawaii. During their stay, three trips were arranged: a boat trip (\(B\)), a coach trip (\(C\)) and a helicopter trip (\(H\)).</p>
<p class="p1">From this group of people:</p>
<table style="width: 691.333px;">
<tbody>
<tr>
<td style="width: 182px; text-align: right;">3 </td>
<td style="width: 526.333px;">went on all three trips;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">16 </td>
<td style="width: 526.333px;">went on the coach trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">13 </td>
<td style="width: 526.333px;">went on the boat trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">5 </td>
<td style="width: 526.333px;">went on the helicopter trip <strong>only</strong>;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;"><em>x </em></td>
<td style="width: 526.333px;">went on the coach trip and the helicopter trip <strong>but not</strong> the boat trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">2<em>x </em></td>
<td style="width: 526.333px;">went on the boat trip and the helicopter trip <strong>but not</strong> the coach trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">4<em>x </em></td>
<td style="width: 526.333px;">went on the boat trip and the coach trip <strong>but not</strong> the helicopter trip;</td>
</tr>
<tr>
<td style="width: 182px; text-align: right;">8 </td>
<td style="width: 526.333px;">did not go on any of the trips.</td>
</tr>
</tbody>
</table>
</div>
<div class="specification">
<p class="p1">One person in the group is selected at random.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Draw a Venn diagram to represent the given information, using sets labelled \(B\)<span class="s1">, </span>\(C\) <span class="s1">and </span>\(H\).</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(x = 3\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of \(n(B \cap C)\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the probability that this person</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>went on at most one trip;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>went on the coach trip, given that this person also went on both the helicopter trip and the boat trip.</p>
<div class="marks">[4]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="images/Schermafbeelding_2017-03-07_om_10.03.03.png" alt="N16/5/MATSD/SP2/ENG/TZ0/02.a/M"> <strong><em>(A5)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for rectangle and three labelled intersecting circles (<span class="s1">U </span>need not be seen),</p>
<p class="p1"><strong><em>(A1) </em></strong>for <span class="s1">3 </span>in the correct region,</p>
<p class="p1"><strong><em>(A1) </em></strong>for <span class="s1">8 </span>in the correct region,</p>
<p class="p1"><strong><em>(A1) </em></strong>for <span class="s1">5</span>, <span class="s1">13 </span>and <span class="s1">16 </span>in the correct regions,</p>
<p class="p1"><strong><em>(A1) </em></strong>for \(x\), \(2x\) and \(4x\) in the correct regions.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(8 + 13 + 16 + 3 + 5 + x + 2x + 4x = 66\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for <strong>either </strong>a completely correct equation <strong>or </strong>adding all the terms from <strong>their </strong>diagram in part (a) and equating to <span class="s1">66</span>.</p>
<p class="p1">Award <strong><em>(M0)(A0) </em></strong>if their equation has no \(x\).</p>
<p class="p1"> </p>
<p class="p1">\(7x = 66 - 45\)<strong> OR</strong> \(7x + 45 = 66\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for adding their like terms correctly, <strong>but only </strong>when the solution to their equation is equal to <span class="s1">3 </span>and is consistent with their original equation.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\(x = 3\) </span><strong><em>(AG)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>The conclusion \(x = 3\) must be seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="s1">15 <span class="Apple-converted-space"> </span></span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Follow through from part (a). The answer must be an integer.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \(\frac{{42}}{{66}}{\text{ }}\left( {\frac{7}{{11}},{\text{ }}0.636,{\text{ }}63.6\% } \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(A1)(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for numerator, <strong><em>(A1) </em></strong>for denominator. Follow through from their Venn diagram.</p>
<p class="p2"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(\frac{3}{9}{\text{ }}\left( {\frac{1}{3},{\text{ }}0.333,{\text{ }}33.3\% } \right)\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator. Follow through from their Venn diagram.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Mike, the laboratory mouse, is placed at the starting point, S, of a maze. Some paths in the maze lead to Trap A, some to Trap B, and others to escape doors. Some paths have one and some have two sections. If his path forks, Mike randomly chooses a path <strong>forward</strong>.</p>
<p class="p1">The following tree diagram represents the maze, showing all possible paths, and the probability that Mike chooses a certain section of a path through the maze.</p>
<p class="p1" style="text-align: center;"><img src="images/Schermafbeelding_2015-12-04_om_09.51.00.png" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down the value of</p>
<p class="p1">(i) <span class="Apple-converted-space"> \(p\)</span> ;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(q\)</span> ;</p>
<p class="p1">(iii) <span class="Apple-converted-space"> \(r\)</span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>Find the probability that Mike reaches Trap B.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>Find the probability that Mike reaches Trap A.</p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>Find the probability that Mike escapes from the maze.</p>
<div class="marks">[7]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Sonya, a lab assistant, counts the number of paths that lead to traps or escape doors. She believes that the probability that Mike will be trapped is greater than the probability that he will escape.</p>
<p class="p1">State whether Sonya is correct. Give a mathematical <span class="s1">justification </span>for your conclusion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">During the <span class="s1">first </span>trial Mike escapes.</p>
<p class="p1">Given that Mike escaped, <span class="s1">find </span>the probability that he went directly from S to Escape Door 3.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\frac{1}{3}\;\;\;(0.333333…,{\text{ }}33.3333...\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\frac{1}{2}\;\;\;(0.5,{\text{ }}50\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>\(\frac{1}{4}\;\;\;(0.25,{\text{ }}25\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\frac{1}{3} \times \frac{1}{4}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\( = \frac{1}{{12}}\;\;\;({\text{0.0833333..., 8.33333...% )}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(G2)</em></strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\frac{1}{3} \times \frac{1}{2} + \frac{1}{3} \times \frac{1}{4} + \frac{1}{3} \times \frac{1}{4}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for their three correct products seen, <strong><em>(M1) </em></strong>for addition of their products.</p>
<p class="p2"> </p>
<p class="p1">\( = \frac{1}{3}\;\;\;(0.333333...,{\text{ }}33.3333...\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their parts (a)(i) and (a)(iii).</p>
<p class="p2"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>\(1 - \frac{1}{{12}} - \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from parts (b)(i) and (b)(ii).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">\(\frac{1}{3} \times \frac{1}{2} + \frac{1}{3} \times \frac{1}{4} + \frac{1}{3}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from parts (a)(i) and (a)(ii).</p>
<p class="p2"> </p>
<p class="p1">\( = \frac{7}{{12}}\;\;\;(0.583333...,{\text{ }}58.3333...\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Sonya is not correct. <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1">The probability that Mike escapes is \(\frac{7}{{12}}\), which is</p>
<p class="p1">greater than \(\frac{5}{{12}}{\text{ }}\left( {{\text{or greater than }}\frac{1}{2}} \right)\). <span class="Apple-converted-space"> </span><strong><em>(R1)</em>(ft)</strong></p>
<p class="p1"><strong>Notes: </strong>Do not award <strong><em>(A1)(R0)</em></strong>.</p>
<p class="p1">Follow through from their answers to part (b).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{{\frac{1}{3}}}{{\frac{7}{{12}}}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1) </em></strong>for correct numerator, <strong><em>(A1) </em></strong>for correct denominator.</p>
<p class="p2"> </p>
<p class="p1">\( = \frac{4}{7}\;\;\;\left( {\frac{{12}}{{21}},{\text{ 0.571428..., 57.1428...% }}} \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (b)(iii).</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A water container is made in the shape of a cylinder with internal height \(h\) cm and internal base radius \(r\) cm.</p>
<p class="p2" style="text-align: center;"><img src="images/Schermafbeelding_2017-03-07_om_08.31.01.png" alt="N16/5/MATSD/SP2/ENG/TZ0/06"></p>
<p class="p1">The water container has no top. The inner surfaces of the container are to be coated with a water-resistant material.</p>
</div>
<div class="specification">
<p class="p1">The volume of the water container is \(0.5{\text{ }}{{\text{m}}^3}\).</p>
</div>
<div class="specification">
<p class="p1">The water container is designed so that the area to be coated is minimized.</p>
</div>
<div class="specification">
<p class="p1">One can of water-resistant material coats a surface area of \(2000{\text{ c}}{{\text{m}}^2}\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Write down a formula for \(A\), <span class="s1">the surface area to be coated.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Express this volume in \({\text{c}}{{\text{m}}^3}\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Write down, in terms of \(r\) </span>and \(h\), an equation for the volume of this water container.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(A = \pi {r^2}\frac{{1\,000\,000}}{r}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find \(\frac{{{\text{d}}A}}{{{\text{d}}r}}\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Using your answer to part (e), find the value of \(r\) <span class="s1">which minimizes \(A\).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the value of this minimum area.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the least number of cans of water-resistant material that will coat the area in <span class="s1">part (g).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\((A = ){\text{ }}\pi {r^2} + 2\pi rh\) </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for either \(\pi {r^2}\) <strong>OR</strong> \(2\pi rh\) seen. Award <strong><em>(A1) </em></strong>for two correct terms added together.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(500\,000\) </span><strong><em>(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Units <strong>not </strong>required.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(500\,000 = \pi {r^2}h\) </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for \(\pi {r^2}h\) equating to their part (b).</p>
<p class="p1"><span class="s1">Do not accept </span>unless \(V = \pi {r^2}h\) is explicitly defined as their part (b).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)\) </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for their \({\frac{{500\,000}}{{\pi {r^2}}}}\) seen.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> \({\frac{{500\,000}}{{\pi {r^2}}}}\) into a <strong>correct </strong>part (a).</p>
<p class="p1">Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to \(\pi rh = \frac{{500\,000}}{r}\) and substituting for \(\pi rh\) <span class="s1">in expression for \(A\).</span></p>
<p class="p3"> </p>
<p class="p4"><span class="Apple-converted-space">\(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\) </span><span class="s2"><strong><em>(AG)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>The conclusion, \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\), must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p4">Accept \({10^6}\) as equivalent to \({1\,000\,000}\).</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(A = \pi {r^2} + 2\pi r\left( {\frac{{500\,000}}{{\pi {r^2}}}} \right)\) </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1)</em>(ft) </strong>for their \({\frac{{500\,000}}{{\pi {r^2}}}}\) seen.</p>
<p class="p1">Award <strong><em>(M1) </em></strong>for correctly substituting <strong>only</strong> \({\frac{{500\,000}}{{\pi {r^2}}}}\) into a <strong>correct </strong>part (a).</p>
<p class="p1">Award <strong><em>(A1)</em>(ft)<em>(M1) </em></strong>for rearranging part (c) to \(\pi rh = \frac{{500\,000}}{r}\) and substituting for \(\pi rh\) <span class="s1">in expression for \(A\).</span></p>
<p class="p3"> </p>
<p class="p4"><span class="Apple-converted-space">\(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\) </span><span class="s2"><strong><em>(AG)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>The conclusion, \(A = \pi {r^2} + \frac{{1\,000\,000}}{r}\), must be consistent with their working seen for the <strong><em>(A1) </em></strong>to be awarded.</p>
<p class="p4">Accept \({10^6}\) as equivalent to \({1\,000\,000}\).</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(2\pi r - \frac{{{\text{1}}\,{\text{000}}\,{\text{000}}}}{{{r^2}}}\) </span><strong><em>(A1)(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(A1) </em></strong>for \(2\pi r\), <strong><em>(A1) </em></strong>for \(\frac{1}{{{r^2}}}\) or \({r^{ - 2}}\), <strong><em>(A1) </em></strong>for \( - {\text{1}}\,{\text{000}}\,{\text{000}}\).</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(2\pi r - \frac{{1\,000\,000}}{{{r^2}}} = 0\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for equating their part (e) to zero.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\({r^3} = \frac{{1\,000\,000}}{{2\pi }}\) <strong>OR</strong> \(r = \sqrt[3]{{\frac{{1\,000\,000}}{{2\pi }}}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for isolating \(r\).</p>
<p class="p2"> </p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">sketch of derivative function <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">with its zero indicated <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\((r = ){\text{ }}54.2{\text{ }}({\text{cm}}){\text{ }}(54.1926 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\pi {(54.1926 \ldots )^2} + \frac{{1\,000\,000}}{{(54.1926 \ldots )}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for correct substitution of their part (f) into the given equation.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 27\,700{\text{ }}({\text{c}}{{\text{m}}^2}){\text{ }}(27\,679.0 \ldots )\) </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(\frac{{27\,679.0 \ldots }}{{2000}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>(M1) </em></strong>for dividing their part (g) by <span class="s1">2000</span>.</p>
<p class="p2"> </p>
<p class="p1"><span class="Apple-converted-space">\( = 13.8395 \ldots \) </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Follow through from part (g).</p>
<p class="p2"> </p>
<p class="p1"><span class="s1">14 </span>(cans) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G3)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: <span class="Apple-converted-space"> </span></strong>Final <strong><em>(A1) </em></strong>awarded for rounding up their \(13.8395 \ldots \) to the next integer.</p>
<p class="p2"> </p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p style="text-align: left;"><span style="font-family: times new roman,times; font-size: medium;">\(50\) students at Rambling High School were asked how they travelled to school yesterday. All of the students travelled by bus, by car or walked.</span></p>
<p style="text-align: left;"><span style="font-family: times new roman,times; font-size: medium;"> \(12\) students travelled by car only</span><br><span style="font-family: times new roman,times; font-size: medium;"> \(7\) students travelled by bus only</span><br><span style="font-family: times new roman,times; font-size: medium;"> \(5\) students travelled by car and walked, but did not use a bus</span><br><span style="font-family: times new roman,times; font-size: medium;"> \(10\) students travelled by bus and walked, but did not use a car</span><br><span style="font-family: times new roman,times; font-size: medium;"> \(3\) students used all three forms of travel.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Represent this information on a Venn Diagram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were \(28\) students who used a bus to travel to school. Calculate the number of students</span><br><span>(i) who travelled by car and by bus but did not walk;</span><br><span>(ii) who travelled by car.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Tomoko used a bus to travel to school yesterday.</span></p>
<p><span>Find the probability that she also walked.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random from all \(50\) students.</span></p>
<p><span>Find the probability that</span><br><span>(i) both students walked;</span><br><span>(ii) only one of the students walked.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt></span><span><span> </span><span> <em><strong>(A4)</strong></em></span></span><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for rectangle and three labelled intersecting circles, <em><strong>(A1)</strong></em> for \(3\), <em><strong>(A1)</strong></em> for \(5\) and \(10\), <em><strong>(A1)</strong></em> for \(7\) and \(12\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(28 - (10 + 3 + 7) = 8\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their Venn diagram.</span></p>
<p><br><span>(ii) \(5 + 3 + 8 + 12 = 28\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from part (b)(i) and their Venn diagram.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({\text{P(}}\left. {{\text{walk}}} \right|{\text{bus}}) = \frac{{13}}{{28}}\) \((0.464{\text{, }}46.4\% )\) (\(0.464285 \ldots \)) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for the numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{23}}{{50}} \times \frac{{22}}{{49}}\) <em><strong>(A1)(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(23\) seen, <em><strong>(M1)</strong></em> for non replacement, <em><strong>(M1)</strong></em> for multiplying their fractions.</span></p>
<p><br><span>\( = \frac{{506}}{{2450}}\) \((0.207{\text{, }}20.7\% )\) (\(0.206530 \ldots \)) <em><strong>(A1)(G3)</strong></em></span></p>
<p><span>(ii) \(\frac{{23}}{{50}} \times \frac{{27}}{{49}} + \frac{{27}}{{50}} \times \frac{{23}}{{49}}\) <strong><em>(A1)</em>(ft)<em>(M1)</em></strong></span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for two products, <em><strong>(M1)</strong></em> for adding two products. Do not penalise in (ii) for consistent use of with replacement.</span></p>
<p><br><span><span>\( = \frac{{1242}}{{2450}}\) \((0.507{\text{, }}50.7\% )\) (\(0.509638 \ldots \)) </span> <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">When Geraldine travels to work she can travel either by car (<em>C</em>), bus (<em>B</em>) or train (<em>T</em>). She travels by car on one day in five. She uses the bus 50 % of the time. The probabilities of her being late (<em>L</em>) when travelling by car, bus or train are 0.05, 0.12 and 0.08 respectively.</span></p>
</div>
<div class="specification">
<p><em><span style="font-size: medium; font-family: times new roman,times;">It is <strong>not</strong> necessary to use graph paper for this question.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Copy the tree diagram below and fill in all the probabilities, where <em>NL</em> represents not late, to represent this information.</span></p>
<p><img src="data:image/png;base64,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" alt></p>
<div class="marks">[5]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Geraldine travels by bus and is late.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Geraldine is late.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Geraldine travelled by train, given that she is late.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Sketch the curve of the function \(f (x) = x^3 − 2x^2 + x − 3\) for values of \(x\) from −2 to 4, giving the intercepts with both axes.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>On the same diagram, sketch the line \(y = 7 − 2x\) and find the coordinates of the point of intersection of the line with the curve.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the value of the gradient of the curve where \(x = 1.7\) .</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><em><span>Award <strong>(A1)</strong> for 0.5 at B, <strong>(A1)</strong> for 0.3 at T, then <strong>(A1)</strong> for each correct pair. Accept fractions or percentages. <strong>(A5)</strong></span></em></p>
<p><em><span><strong>[5 marks]<br></strong></span></em></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.06 (<em>accept</em> \(0.5 \times 0.12\) <em>or</em> 6%) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><em>[1 mark]</em><br></strong></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>for a relevant two-factor product, either</em> \(C \times L\) <em>or</em> \(T \times L\) </span><span><em><strong>(M1)</strong></em></span></p>
<p><span> <em>for summing three two-factor products </em> <em><strong>(M1)</strong></em></span></p>
<p><span>\((0.2 \times 0.05 + 0.06 + 0.3 \times 0.08)\)</span></p>
<p><span>0.094 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{0.3 \times 0.08}}{{0.094}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em><em>award <strong>(M1)</strong> for substituted conditional probability formula seen, </em></em></span><span><em><strong>(A1)</strong></em><strong>(ft) </strong></span><span><em><em>for correct substitution</em></em></span></p>
<p><span>= 0.255<em><em> <strong>(A1)</strong></em></em><strong>(ft)</strong><em><em><strong>(G2)</strong><br></em></em></span></p>
<p><span><em><em><strong>[3 marks]<br></strong></em></em></span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt> <em><strong><span>(G3)</span></strong></em></p>
<p><em><strong><span>[3 marks]<br></span></strong></em></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>line drawn with <strong>–ve</strong> gradient and <strong>+ve</strong> y-intercept</em> <strong><em>(G1)</em></strong></span></p>
<p><span>(2.45, 2.11) <em><strong>(G1)(G1)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(f ' (1.7) = 3(1.7)^2 - 4(1.7) + 1\) <em><strong>(M1)</strong></em><br></span></p>
<p><em><span>award <strong>(M1)</strong> for substituting in their</span></em><span> \(</span><span><span>f</span></span><span><span><span>' </span> </span> (x)\)</span></p>
<p><span>2.87 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The curve sketching and straight line were well drawn but not all candidates indicated the intersection points with the axes. In finding the line / curve intersection some candidates did not use the intersection function on the GDC. Few candidates managed the last part. Many just chose two sets of coordinates and used the gradient formula.</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The curve sketching and straight line were well drawn but not all candidates indicated the intersection points with the axes. In finding the line / curve intersection some candidates did not use the intersection function on the GDC. Few candidates managed the last part. Many just chose two sets of coordinates and used the gradient formula.</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This should have been an easy first question but, even so, there were some candidates who were unable to fill in the tree diagram correctly let alone evaluate any probabilities. The majority of candidates were confident with answering parts (a), (b) and (c) but the conditional probability question was not well answered with few candidates managing to recognise that it was a conditional type.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The curve sketching and straight line were well drawn but not all candidates indicated the intersection points with the axes. In finding the line / curve intersection some candidates did not use the intersection function on the GDC. Few candidates managed the last part. Many just chose two sets of coordinates and used the gradient formula.</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">100 students at IB College were asked whether they study Music (<em>M</em>), Chemistry (<em>C</em>), or Economics (<em>E</em>) with the following results.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">10 study all three</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">15 study Music and Chemistry</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">17 study Music and Economics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">12 study Chemistry and Economics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">11 study Music <strong>only</strong></span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">6 study Chemistry <strong>only</strong></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to represent the information above.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of students who study Music but not Economics.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There are 22 Economics students <strong>in total</strong>.</span></p>
<p><span>(i) Calculate the number of students who study Economics only.</span></p>
<p><span>(ii) Find the number of students who study none of these three subjects.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A student is chosen at random from the 100 that were asked above.</span></p>
<p><span>Find the probability that this student</span></p>
<p><span>(i) studies Economics;</span></p>
<p><span>(ii) studies Music and Chemistry but not Economics;</span></p>
<p><span>(iii) does not study either Music or Economics;</span></p>
<p><span>(iv) does not study Music given that the student does not study Economics.</span></p>
<div class="marks">[7]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for rectangle and three labelled circles (<em>U</em> need not be seen)</span></p>
<p><span><em><strong>(A1)</strong></em> for 10 in the correct region</span></p>
<p><span><em><strong>(A1)</strong></em> for 2, 7 and 5 in the correct regions</span></p>
<p><span><em><strong>(A1)</strong></em> for 6 and 11 in the correct regions <em><strong>(A4)</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>16 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><br>Note: </strong>Follow through from their Venn diagram.<strong><br></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(10 + 7 + 2\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for summing their 10, 7 and 2.</span></p>
<p><br><span>\(22 - 19\)</span></p>
<p><span>\(= 3\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their diagram. Award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> for answers consistent with their diagram irrespective of whether working seen. Award a maximum of <em><strong>(M1)(A0)</strong></em> for a negative answer.</span></p>
<p><br><span>(ii) \(22 + 11+ 5 + 6\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for summing 22, and their 11, 5 and 6.</span></p>
<p><br><span>\(100 - 44\)</span></p>
<p><span>\(= 56\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from their diagram. Award <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong> for answers consistent with their diagram <strong>and</strong> the use of 22 irrespective of whether working seen. If negative values are used or implied award <em><strong>(M0)(A0)</strong></em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{22}}{{100}}\left( {\frac{{11}}{{50}},0.22,22\% } \right)\) <em><strong>(A1)(G1)</strong></em></span></p>
<p><span>(ii) \(\frac{{5}}{{100}}\left( {\frac{{1}}{{20}},0.05,5\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for their 5 in numerator, <em><strong>(A1)</strong></em> for denominator. </span></p>
<p><span> Follow through from their diagram.</span></p>
<p><span><br>(iii) \(\frac{{62}}{{100}}\left( {\frac{{31}}{{50}},0.62,62\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></span><br><br></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for \(100 - (22 + 11 + {\text{their }}5)\), <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span> Follow through from their diagram.<br><br></span></p>
<p><span>(iv) \(\frac{{62}}{{78}}\left( {\frac{{31}}{{39}},0.795,79.5\% } \right)\) (0.794871...) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)<br><br></strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for numerator, <em><strong>(A1)</strong></em> for denominator. Follow</span></p>
<p><span>through from part (d)(iii) for numerator.</span></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question divided the candidates into two parts: those who knew how to interpret the information in a manner the led to a consistent Venn diagram and those who did not. The use of the word “only” is crucial in this regard.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">Follow through to the probability part of the question was contingent on the use of the given \(n(E) = 22\) ; given information should be used in subsequent parts. As ever, conditional probability proves a trial for many.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">It is recommended that candidates write probabilities as unsimplified fractions as this increase their chances of gaining follow through from previous parts.</span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Jorge conducted a survey of \(200\) drivers. He asked two questions:</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">How long have you had your driving licence?</span><br><span style="font-family: times new roman,times; font-size: medium;">Do you wear a seat belt when driving?</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The replies are summarized in the table below.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Jorge applies a \({\chi ^2}\) test at the \(5\% \) level to investigate whether wearing a seat belt is associated with the time a driver has had their licence.</span></p>
<p><span>(i) Write down the null hypothesis, \({{\text{H}}_0}\).</span></p>
<p><span>(ii) Write down the number of degrees of freedom.</span></p>
<p><span>(iii) Show that the expected number of drivers that wear a seat belt and have had their driving licence for more than \(15\) years is \(22\), correct to the nearest whole number.</span></p>
<p><span>(iv) Write down the \({\chi ^2}\) test statistic for this data.</span></p>
<p><span>(v) Does Jorge accept \({{\text{H}}_0}\) ? Give a reason for your answer.</span></p>
<div class="marks">[8]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Consider the \(200\) drivers surveyed. One driver is chosen at random. Calculate the probability that</span></p>
<p><span>(i) this driver wears a seat belt;</span></p>
<p><span>(ii) the driver does not wear a seat belt, <strong>given that</strong> the driver has held a licence for more than \(15\) years.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two drivers are chosen at random. Calculate the probability that</span></p>
<p><span>(i) both wear a seat belt.</span></p>
<p><span>(ii) at least one wears a seat belt.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \({{\text{H}}_0} = \) wearing of a seat belt and the time a driver has held a licence are independent. <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note: </strong>For independent accept 'not associated' but do not accept 'not related' or 'not correlated'</span></p>
<p><br><span>(ii) \(2\) <em><strong>(A1)</strong></em></span></p>
<p><span>(iii) \(\frac{{98 \times 45}}{{200}} = 22.05 = 22\) (<em>correct to the nearest whole number</em>) <em><strong>(M1)(A1)(AG)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for correct formula and <em><strong>(A1)</strong></em> for correct substitution. Unrounded answer must be seen for the <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><br><span>(iv) \({\chi ^2} = 8.12\) <em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note: </strong>For unrounded answer award <em><strong>(G1)(G0)(AP)</strong></em>. If formula used award <em><strong>(M1)</strong></em> for correct substituted formula with correct substitution (6 terms) <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><br><span>(v) “Does not accept \({{\text{H}}_0}\)” <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>\(p{\text{-}}value < 0.05\) <em><strong>(R1)</strong></em><strong>(ft)</strong></span></p>
<p><br><span><strong>Note: </strong>Allow “Reject \({{\text{H}}_0}\)” or equivalent. Follow through from their \({\chi ^2}\) statistic. Award <strong><em>(R1)</em>(ft)</strong> for comparing the appropriate values. The <strong><em>(A1)</em>(ft)</strong> can be awarded only if the conclusion is valid according to the comparison given. If no reason given or </span><span>if reason is wrong the two marks are lost.</span></p>
<p><span><em><strong>[8 marks]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{98}}{{200}}( = 0.49{\text{, }}49\% )\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><br><span>(ii) \(\frac{{15}}{{45}}( = 0.333{\text{, }}33.3\% )\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{98}}{{200}} \times \frac{{97}}{{199}} = 0.239{\text{ }}(23.9\% )\) <em><strong>(A1)(M1)(A1)(G3)</strong></em></span></p>
<p><br><span><strong>Note: <em>(A1)</em></strong> for correct probabilities seen, <em><strong>(M1)</strong></em> for multiplying two probabilities, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><br><span>(ii) \(1 - \frac{{102}}{{200}} \times \frac{{101}}{{199}} = 0.741{\text{ }}(74.1\% )\) <em><strong>(M1)(M1)(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for showing the product, <em><strong>(M1)</strong></em> for using the probability of the complement, <em><strong>(A1)</strong></em> for correct answer. Follow through for </span><span>consistent use of with replacement.</span></p>
<p><br><span><strong>OR</strong></span></p>
<p><span>\(\frac{{98}}{{200}} \times \frac{{97}}{{199}} + \frac{{98}}{{200}} \times \frac{{102}}{{199}} + \frac{{102}}{{200}} \times \frac{{98}}{{199}} = 0.741{\text{ }}(74.1\% )\) <em><strong>(M1)(M1)(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for adding three products of fractions (or equivalent), <em><strong>(M1)</strong></em> for using the correct fractions, <em><strong>(A1)</strong></em> for correct answer. Follow through for consistent use of with replacement.</span></p>
<p><span><em><strong>[6 marks]</strong></em><br></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first part of the question was relatively well done. The null hypothesis and the degrees of freedom were well answered by the majority of the students. In the show that question some students used the GDC to find the expected values table and highlighted the correct value \(22.05\). This procedure gained no mark; the expected value formula was expected to be used here. Also those who did use the formula were expected to show the unrounded value \(22.05\) to gain full marks in this part question. Many lost the answer mark for not doing so. GDC was used by most of the students to find the chi-squared test though some students attempted to find this value by hand which made them waste time. Correct values were compared when deciding whether to accept or not the null hypothesis and follow through marks were awarded from their degrees of freedom and chi-squared test when incorrect.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The second part was not as successful as the first one. Simple probability was well answered. Not all the students changed the denominator to \(45\) for the second probability showing their weaknesses in conditional probability. It would have been useful for the students to use a tree diagram to help them solve the last part of this question but very few did so. Some of those students that reached the last part of the question forgot to add one of the three terms. Very few used the probability of the complement.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first part of the question was relatively well done. The null hypothesis and the degrees of freedom were well answered by the majority of the students. In the show that question some students used the GDC to find the expected values table and highlighted the correct value \(22.05\). This procedure gained no mark; the expected value formula was expected to be used here. Also those who did use the formula were expected to show the unrounded value \(22.05\) to gain full marks in this part question. Many lost the answer mark for not doing so. GDC was used by most of the students to find the chi-squared test though some students attempted to find this value by hand which made them waste time. Correct values were compared when deciding whether to accept or not the null hypothesis and follow through marks were awarded from their degrees of freedom and chi-squared test when incorrect.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The second part was not as successful as the first one. Simple probability was well answered. Not all the students changed the denominator to \(45\) for the second probability showing their weaknesses in conditional probability. It would have been useful for the students to use a tree diagram to help them solve the last part of this question but very few did so. Some of those students that reached the last part of the question forgot to add one of the three terms. Very few used the probability of the complement.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The first part of the question was relatively well done. The null hypothesis and the degrees of freedom were well answered by the majority of the students. In the show that question some students used the GDC to find the expected values table and highlighted the correct value \(22.05\). This procedure gained no mark; the expected value formula was expected to be used here. Also those who did use the formula were expected to show the unrounded value \(22.05\) to gain full marks in this part question. Many lost the answer mark for not doing so. GDC was used by most of the students to find the chi-squared test though some students attempted to find this value by hand which made them waste time. Correct values were compared when deciding whether to accept or not the null hypothesis and follow through marks were awarded from their degrees of freedom and chi-squared test when incorrect.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The second part was not as successful as the first one. Simple probability was well answered. Not all the students changed the denominator to \(45\) for the second probability showing their weaknesses in conditional probability. It would have been useful for the students to use a tree diagram to help them solve the last part of this question but very few did so. Some of those students that reached the last part of the question forgot to add one of the three terms. Very few used the probability of the complement.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">In a college 450 students were surveyed with the following results</span></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">150 have a television</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">205 have a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">220 have an iPhone</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">75 have an iPhone and a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">60 have a television and a computer</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">70 have a television and an iPhone</span></em></p>
<p style="margin-left: 30px;"><em><span style="font-size: medium; font-family: times new roman,times;">40 have all three.</span></em></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn diagram to show this information. Use <em>T</em> to represent the set of students who have a television,<em> C</em> the set of students who have a computer and <em>I</em> the set of students who have an iPhone.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of students that</span></p>
<p><span>(i) have a computer only;</span></p>
<p><span>(ii) have an iPhone and a computer but no television.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n[T \cap (C \cup I)']\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of students who have none of the three.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random from the 450 students. Calculate the probability that</span></p>
<p><span>(i) neither student has an iPhone;</span></p>
<p><span>(ii) only one of the students has an iPhone.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The students are asked to collect money for charity. In the first month, the students collect <em>x</em> dollars and the students collect <em>y</em> dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be represented by the equation <em>x</em> + 5<em>y</em> = 7650.</span></p>
<p><span>In the first 10 months they collect 13 050 dollars.</span></p>
<p><span>(i) Write down a second equation in <em>x</em> and <em>y</em> to represent this information.</span></p>
<p><span>(ii) Write down the value of <em>x</em> and of <em>y </em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The students are asked to collect money for charity. In the first month, the students collect <em>x</em> dollars and the students collect <em>y</em> dollars in each subsequent month. In the first 6 months, they collect 7650 dollars. This can be represented by the equation <em>x</em> + 5<em>y</em> = 7650.</span></p>
<p><span>In the first 10 months they collect 13 050 dollars.</span></p>
<p><span>Calculate the number of months that it will take the students to collect 49 500 dollars.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt><span> <em><strong>(A1)(A1)(A1)(A1)</strong></em></span></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for labelled sets <em>T</em>, <em>C</em>, and <em>I</em> included inside an enclosed universal set. (Label <em>U</em> is not essential.) Award <em><strong>(A1)</strong></em> for central entry 40. <em><strong>(A1)</strong></em> for 20, 30 and 35 in the other intersecting regions. <em><strong>(A1)</strong></em> for 60, 110 and 115 or <em>T</em>(150), <em>C</em>(205), <em>I</em>(220).</span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>In parts (b), (c) and (d) follow through from their diagram.<br></span></strong></em></p>
<p><em><strong><span> </span></strong></em></p>
<p><span>(i) 110 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span>(ii) 35 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>In parts (b), (c) and (d) follow through from their diagram.</span></strong></em></p>
<p><em><strong><span> </span></strong></em></p>
<p><span>60</span><em><strong><span> (A1)</span></strong></em><strong><span>(ft)</span></strong><em><strong><span><br></span></strong></em></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span>In parts (b), (c) and (d) follow through from their diagram.</span></strong></em></p>
<p><em><strong><span> </span></strong></em></p>
<p><span>450 </span><span><span>− </span>(60 </span><span><span>+ </span>20 </span><span><span>+ </span>40 </span><span><span>+ </span>30 </span><span><span>+ </span>115 </span><span><span>+ </span>35 </span><span><span>+ </span>110) <strong><em>(M1)</em></strong> </span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for subtracting all their values from 450.<br></span></p>
<p><span> </span></p>
<p><span>= 40 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{230}}{{450}} \times \frac{{229}}{{449}}\) <em><strong>(A1)(M1)</strong></em></span> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct fractions, <em><strong>(M1)</strong></em> for multiplying their fractions.</span></p>
<p> </p>
<p><span>\(\frac{{52670}}{{202050}}\left( {\frac{{5267}}{{20205}},{\text{ 0}}{\text{.261, 26}}{\text{.1% }}} \right)(0.26067...)\) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><strong><span><strong>Note:</strong></span></strong><span> Follow through from their Venn diagram in part (a).</span></span></p>
<p><span> </span></p>
<p><span>(ii) \(\frac{{220}}{{450}} \times \frac{{230}}{{449}} + \frac{{230}}{{450}} \times \frac{{220}}{{449}}\) <em><strong>(A1)(A1)</strong></em><br></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for addition of their products, <em><strong>(A1)</strong></em> for two correct products.<br></span></p>
<p><span> </span></p>
<p><span><strong>OR</strong><br></span></p>
<p><span>\(\frac{{230}}{{450}} \times \frac{{220}}{{449}} \times 2\) <em><strong>(A1)(A1)</strong></em> <br></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em> for their product of two fractions multiplied by 2, <em><strong>(A1)</strong></em> for correct product of two fractions multiplied by 2. Award <em><strong>(A0)(A0)</strong></em> if correct product is seen not multiplied by 2.<br></span></p>
<p><span> </span></p>
<p><span>\(\frac{{2024}}{{4041}}(0.501,{\text{ 50}}{\text{.1% )(0}}{\text{.50086}}...{\text{)}}\) <em><strong>(A1)(G2)</strong></em><br></span></p>
<p><span><strong>Note:</strong> Follow through from their Venn diagram in part (a) and/or their 230 used in part (e)(i).</span></p>
<p><span><strong>Note:</strong> For consistent use of replacement in parts (i) and (ii) award at most <em><strong>(A0)(M1)(A0)</strong></em> in part (i) and <em><strong>(A1)</strong></em><strong>(</strong><strong>ft)</strong><em><strong>(A1)(A1)</strong></em><strong>(ft)</strong> in part (ii).<br></span></p>
<p><span> </span></p>
<p><span><em><strong>[6 marks]</strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) <em>x</em> + 9<em>y</em> = 13050 <em><strong>(A1)</strong></em><br></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span>(ii) <em>x</em> = 900 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>y</em> = 1350 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Follow through from their equation in (f)(i). Do not award <em><strong>(A1)</strong></em><strong>(ft)</strong> if answer is negative. Award <em><strong>(M1)(A0)</strong></em> for an attempt at solving simultaneous equations algebraically but incorrect answer obtained.</span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>49500 = 900 + 1350<em>n</em> <em><strong>(A1)</strong></em><strong>(ft)</strong></span> </p>
<p><span><strong>Notes:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for setting up correct equation. Follow through from candidate’s part (f).</span></p>
<p> </p>
<p><span><em>n</em> = 36 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>The total number of months is 37. <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for 36 seen as final answer with no working. The value of <em>n</em> must be a positive integer for the last two <em><strong>(A1)</strong></em><strong>(ft)</strong> to be awarded.</span></p>
<p> </p>
<p><span><strong>OR</strong> </span></p>
<p><span>49500 = 900 + 1350(<em>n</em> − 1) <em><strong>(A2)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Award <em><strong>(A2)</strong></em><strong>(ft)</strong> for setting up correct equation. Follow through from candidate’s part (f).</span></p>
<p> </p>
<p><span><em>n</em> = 37 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> The value of <em>n</em> must be a positive integer for the last <em><strong>(A1)</strong></em><strong>(ft)</strong> to be awarded.</span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. The majority of candidates answered part (a) and at least parts of (b), and (d). <br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. The majority of candidates answered part (a) and at least parts of (b), and (d). <br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. Part (c) proved to be difficult, as it required understanding and interpreting set notation. <br></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. The majority of candidates answered part (a) and at least parts of (b), and (d). <br></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. Part (e) was rarely answered in its entirety. <br></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. Part (f) was answered by many candidates, but most of them offered a partial answer to part (g); a typical response was 36 instead of 37.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The question was moderately well answered. Part (f) was answered by many candidates, but most of them offered a partial answer to part (g); a typical response was 36 instead of 37.</span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The figure below shows the lengths in centimetres of fish found in the net of a small trawler.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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7BdvIKadskxijDjwTNYHW2QrAZq2j6gq2jhQU07A0/Z1mdCGMPqaINkNVDT9gFdRQsPano9dV0fdvuf+71t27IsT3E8M9KDuWl7JKuBmrYP6CpaeFDT62nbVs26q08bNgk1bY9kNVDT9gFdRQsPatorrI42SFYDNW0f0FW08KCmvcLqaINkNVDT9gFdRQsPatoTTHrYI1kN1LR9QFfRwoOa9gQ1bY9kNVDT9gFdRQsPatorrI42SFYDNW0f0FW08KCmvcLqaINkNVDT9gFdRQsPatoTTHrYI1kN1LR9QFfRwoOa9gQ1bY9kNVDT9gFdRQsPatorrI42SFYDNW0f0FW08KCmvcLqaINkNVDT9gFdRQsPatoN+S3/ud9frsbqaINkNVDT9gFdRQsPatoBj6I47PaXNJ1Zh7lpeySrgZq2D+gqWnhQ07a0bYu5EKnprZGsBmraPqCraOFBTVvR9/05SaqqeqlpwOpog2Q1UNP2AV1FCw9q2oqf+/2aZcMwUNMekKwGato+oKto4UFNr6dpmmMU9X0/zGpaT3ewOtogWQ3UtH1AV9HCg5peSd/3xyhSUwFQ0x6QrAZq2j6gq2jhQU2v5Jpl+gg8Jj08IFkN1LR9QFfRwoOaXkPbtuM+Ml5LptryVs7AkKwGato+oKto4UFNr6HrukdR6K/Dbn+K40dRcGbx7ZCsBmraPqCraOFBTbvhZdKDuWl7JKuBmrYP6CpaeFDTbqCmPSBZDdS0fUBX0cKDmnbDJU35TI+tkawGato+oKto4UFNe4XV0QbJaqCm7QO6ihYe1LQnmPSwR7IaqGn7gK6ihQc17Qlq2h7JaqCm7QO6ihYe1LRXWB1tkKwGato+oKto4UFNe4XV0QbJaqCm7QO6ihYe1LRXWB1tkKwGato+oKto4UFNe4K5aXskq4Gatg/oKlp4UNOeoKbtkawGato+oKto4UFNe4XV0QbJaqCm7QO6ihYe1LQDmqZp23bJmqyONkhWAzVtH9BVtPCgpq3ABC6oZJc0nZE1kx72SFYDNW0f0FW08KCm14MJXK5ZVtf1NcsOu31+y5+tTE3bI1kN1LR9QFfRwoOaXk/TNHVd4++u6w67/TGK5j/C6miDZDVQ0/YBXUULD2raGYfd/uVD8lgdbZCsBmraPqCraOFBTbuhLMtzkmCW8RlYHW2QrAZq2j6gq2jhQU3b0rYtEtP6ROMKPSX9bbnpyW23f7ktntto1LRNQFfRwoOatqXrOnSlUdWMDjU1TU3/erRB9sYO1PQrqGlnoE9dVdXMOl9VHZ1vrGQ1UNP2AV1FCw9q2hlN0xx2+0dRzKzzVdWRmhYSbZC9scOXtYsVUNPOgKbVEL1Jvqo6UtNCog2yN3b4snaxAmp6PV3X1XWtktHXLDsnybOVvzY3LTagZHMJ96Dw4oUHNb2en/v9sNsfoyi/5ac4nh+QR01LCyjZXMI9KLx44UFNr6fv+7quH0XxKAo+emkMNS0k2iB7Y4cvaxcroKa98lXVkZoWEm2QvbHDl7WLFVDTnmDSQ1pAyeYS7kHhxQsPatoT1LS0gJLNJdyDwosXHtS0V76qOlLTQqINsjd2+LJ2sQJq2itfVR2paSHRBtkbO3xZu1gBNe2Vr6qO1LSQaIPsjR2+rF2sgJr2BHPT0gJKNpdwDwovXnhQ056gpqUFlGwu4R4UXrzwoKa98lXVkZoWEm2QvbHDl7WLFVDTDlh4C+LwZdWRmhYSbZC9scOXtYsVUNNWqAkBTnH8c7/zmR461LSQaIPsjR2o6VdQ0+upquqw21+zLL/lqGczD5umpqUFlGwu4R4UXrzwoKbXc04SNflh27aH3f4YRfOz1n5VdaSmhUQbZG/s8GXtYgXU9HqM+bSQ/ei6buYjX1UdqWkh0QbZGzt8WbtYATXtjGuWneJ4fp2vqo7UtJBog+yNHb6sXayAmnbGMYrGuWk9JS0/Nz1ZWsuX8+JJjkZNWwaUWfF+HWraDY+iOMXxODH9WRVIeGv5HnNR06Iq3q9DTTugbdtTHC8ZPS28AklWg/OAks31nZqWGU0C1LQtfd+f4ti4nPgM4RVIeGuRXDxq2j6gzGgSoKat6Pv+nCS6o+f71MIrkPDWIrl41LR9QJnRJEBNrweOzm9584eqqs5JMrnyR2TNhLcWycWjpu0DyowmAWp6JXD0+MJFWZaT61PT0gJKNtdHeFB48VxFkwA1vZKu6x5FMX599F2IwluL5OJR0/YBZUaTADXtFeEVSHhrkVw8ato+oMxoEqCmPcGkh7SAks31ER4UXjxX0SRATXuCmpYWULK5PsKDwovnKpoEqGmvCK9AwluL5OJR0/YBZUaTADXtFeEVSHhrkVw8ato+oMxoEqCmvSK8AglvLZKLR03bB5QZTQLUtCeYm5YWULK5PsKDwovnKpoEqGlPUNPSAko210d4UHjxXEWTADXtFeEVSHhrkVw8ato+oMxoEqCm3bDkKaaD+AokvLVILh41bR9QZjQJUNO2VFV1iuNLms6vxqSHtICSzfURHhRePFfRJEBNW/EoimuWHXZ7anrraM4DSjbXR3hQePFcRZMANW1L13VLNA2EVyDhrUVy8ahp+4Ayo0mAmnYANe0hmvOAks31ER4UXjxX0SRATTuAmvYQzXlAyeb6CA8KL56raBKgph0wr2k9Ky28AglvLZKLR03bB3QbbYuXqxK+CzXtAGraQzTnASWb61M86Dag22jUNPkb85o21qSmhQSUbK5P8aDbgDKjbRdzOdS0A5ZoWsI5+SXCW4vk4lHT9gFlRtsu5nKoaQdQ0x6iOQ8o2Vwf4UHhxXMVbbuYy6GmHcCkh4dozgNKNtdHeFB48VxF2y7mcqhpKzC/+GG3P8Vx0zTz04oPv32wXyK8tUguHjVtH1BmtO1iLoeatqJpmkdRqFfXdfPrU9NyAko210d4UHjxXEXbLuZyqGlPMDctLaBkc32EB4UXz1W07WIuh5r2BDUtLaBkc32EB4UXz1W07WIuh5r2CjUtJ6Bkc32EB4UXz1W07WIuh5r2CjUtJ6Bkc32EB4UXz1W07WIuh5r2CjUtJ6Bkc32EB4UXz1W07WIuh5r2BHPT0gJKNtdHeFB48VxF2y7mcqhpT1DT0gJKNtdHeFB48VxF2y7mcqhpr1DTcgJKNtdHeFB48VxF2y7mcqhpr1DTcgJKNtdHeFB48VxF2y7mcqhpTzDpIS2gZHN9hAeFF89VtO1iLoea9gQ1LS2gZHN9hAeFF89VtO1iLoea9go1LSegZHN9hAeFF89VtO1iLoea9go1LSegZHN9hAeFF89VtO1iLudbNK3nHPjiiy++BL6e6Yua5osvvvgS8Xqmr2/RtMLYHfNvjSXz/303mvOAzovnefM33Tlbr//pO+etzXk3mufNcV68d+Nbbt0YalrW4RFVPM+bv7WJPmvne97Ytzbn3WieN8d58d6Nb7l1Y6hpWYdHVPE8b/7WJvqsne95Y9/anHejed4c58V7N77l1o35Ok2/y8s9+FYcV9GMsN8QzXlAydGcB5QczXlA58VzHvPdaNT0C5bs0KZp8lv+KIqZKWupaWkBJUfbIiD5XKhpW5qmOez2VVXVdX2MorquZ1Zm2yOEvAs1bUXf98co+rnf8Ta/5Yfdvm3bZ+tT04SQd6Gmrfi53w+7fdM0eIuedX7Ln61PTRNC3oWatuKcJIfdvus6teSw25/ieLzmRrlpQkjwUNNWLBn6oy+31HTf94+iGCdV2rbNb/l8WnxM13VlWU5+qm3bR1Hop58l1HX97FN1XZdl+VY0RX7Lq6oyov3c7+pHzBK6rnsUhXqp5X3fV1WV3/KZy78zYJNV1msYhrZtf+73t45FWZZ62fR92Pc9/vtW8bCx1yyrqsr4YFVV1yx7q3h1XV+zbPJTiLaweNhXRjnzW37NMqPOYKsvaWoc9zFVVek7f/jTRoyF+nfN5CTx2fGXYg+UZWlsJso5HxNt01ih67qf+31yA/Gv/Jbr+4SatmK5ppf8d55HURyjSM+xAFy6RH29pOlMjdFBGh2vYxTpMR9FcYpjtBOjXc1wSVMV0Ej7nJMEyjjF8bvnkkdRHHZ7vRhlWSJOfssvabrQX/r2XtLUKFtd16c4Xr6xwzC0bXtJ00ua6rtOXU9efizwEeOFD/Z9rxdv4a5Tl7K7rrtmmb6xOLI4yV3SdMlpuK5rbFHbtuckOSeJ2uFVVaHm4MjObGzXdac4NvY8ruvgnKRf4BmGIb/l5ySBWPHHOGbTNPgtq8es63q8EN+F44uSjCU+DENZlmhfxlkcAfEv48qTqgDnJJmMeUnTcZvFhp/i+OU+USWhpq3wqWl0kYxDjsOptHiKY6OCTtI0DZorTt26WJVo1N9L5PUoCjR71SBV00J8tG2Uf3knvW1bo+W0bXvY7dExR52euRKgwF5q/mCUDW+rqhqfAmcKNj4bGeVZeCzyW57fclW2n/tdJc1wanl3113SVCkD5YRZcDTf3XW66PX6YFS8c5JM5vp0zkmi7xAoDH/rO1+dGJaUc2zkyYXXLDtGEfbkzIEeV3h0lvu+R0dbP+h4q+/byb7/uM3+3O/qK4zGou+TsizVB6lpKyARfQlOvOM1nSQ9xjUMolH9LLx92YmrqkoPom/FOUlUhR6WNb9hGHR96O7ruu6w21+zDP+CNSb7HWPQkUGjVdX6mmVGtVYimwGdMqM3apSt7/v5y79GwfR+JVh3LIxc0DXLsH9QPFWe5bsO3TSUDXsPu8vYdXg7v+uwT3RtqUsvxsXzsYzGoO+pb47aOn1j0XtVBcMhXhJTL6S+0PgubJQ67jpjTRv5nGMUqdaNHrH+r3OSjGPqth2Dn8iT5dT3CTVtBeq6aoo4zJM1wImmEV8/5EYlRmt5Nwt8zTJV4YwqjvhvJan13hzOK0Y7X9LHHIbh535HHD2CsQOX2AHVHS/9t7lxAhieX/4dFwxdp67rjJ/Aul/QPt86FjAIYq7eddgnyBXoP/BX7DrUN/3cAIeON3Zc2jG6UrFzJrfOOArG+WAm5jjUs7I9O9Avfz5e0hStG2uOW8qzmJPlRypG9cFn9gk1bQVqgNrReDuTQ3SuaSPg8jSFjmrM48qH89DCVACSiccoUvIaZ5YX7gGkZWABQ9N6A1vimr7vkT9VSUYUb1w2/AJ9WTbEwe8M7C6cxoyfViuOBZK8+qat2HWDloifcRPiz+e7cYYz+owow4qN1ZX6bOtwojLy6ZaaXr4n57cCZcMeGw+9fVfTqJC4qqSXUz+vH/78NKembcG+btvWuNVlEoGaRnXRP75a0z/3+6QKdRcs2QPYk8r1hqaXt+FxWPgLHaLVHoSjcQpBX0/1+i2Phcp4TG7a8soD3esHYniy614OpcAew5gE/A1rr9jYsabHW4cf/jI1rQ8gGa/5LP82o2l1NkUDmTni1LQtfd/jCJ3i+GVm07mmjQ7guEbOg59dqiWPGwk27a2hbygDKvSkpl8mFpBKVqPTUCRslI2mwSmO0UOZ/I358uiMz2Rqi4xjMY4/j57xGJ7susnspwEGYHRdh992+Huw2HVN0+D8oZ+TjM7jko0da1o/SaitM8ppn/SYPNDvJj30n3eTa65Iegx/Mm8zjYVJj03o+37yh+Rhm9y0cSHo3d7lOUmM/tSkpt8t5zGK0GM18r/jn7STXLSxfcZ+M1RoXBZbAsaiDVMtbUnZkAeYHLEweSyWD0DUMx7Dk103ednDQO8uwNT4Ha3SymDFrsMZDh9BT1B9/N1LiMbO1y/nqvOo+tRkL3UcU3GYuoS4ZE8+03TbtsaIw3FNNq4oGjFn9oz6CW4ccV5C3ASVmZ1s6htp2siGY+DRklBjR6MWovWqhc82Zx41yNcYPqGPCVuOXnf1YSTDMGDExVvR0E/H3/rWLS8bhlLoAbGBk8di+W0pesZj+JP5UTbRh6nNY4xgUxtlDOlbOF5QgT6pKoBRnkuavvyRZChV3zp91xnlnB+Qt0TTwzCc4ljVE5R88vQ5qWnD0UvIAIIAAAW/SURBVKofpm8ylDrZDcfXPdO0kd8b7xMOyHNMVVXqF/qzdSw1PdlnQRXs+x69hiXdNzWkTCUW1PAM/eK++vn8MmBd1/p1VP1U8XO/q4o42aheYnSFUJVx96BexZ+BO+UwXPpRFPpAOl09y8umD+FA+1T7XB0LY/lLjIwHwGgtJYUlXelhGNBXwDaiGPgbuw7FW35kVczxSQI/I9q2RZ15eSAm8ySIqY9I0cuJPTBzqpscBjfODukdVXVaHTPWNEbu407LR1Hkt1yNzdBbCtJ0k+Uc/6hCHNxkgA++3CfUtGO20zRuIUNaTe/04WyP18KOKrrMxks1WpzGL2k6TonMB1TFMH4eoj0j4Ls3oA9/1/Twp+Xgi5YUD5uDLO34pnB0z3Gz3/Ky4U5I9JeNsr17LFQhJ3uj8COKt7Bjri6WwOz6SV0VbzyK/BkQkxFH/yKIcj4a7tjEUTgniZ5/x6H8ud/1rUM54cdn9lf3W6OHocbp6wv19XFmQoZhck/q113VZ9XNh+qlnzYQE/tnspzoIlzSVH/gATouzyqkvk/UQmraMZv2pmdYeI/4Qrque+u6HArQNM2zYrRt67yEb60//ySHFSePmZgrttQYgm38a13xSDBQ044Za3ryUhghhCyEmnYMNU0IcQs17ZjfSnoQQkKFmn6b+d4xNU0IcQs1/TbrNM2kByFkHdS0Y6hpQohbqGnHMOlBCHELNe0MTIKHUeuPJ7PDUdOEkHehpp2BW0IU1DQhxAnUtCeYmyaErIOa9gQ1/Ss0f8ftDetLwFMmFk7/CPq+f2v9GZ49v4J8FtS0V6hpz6jnVR12e/3xN35omgZPeV7+XEA8dchVOTE1j/+TE3ELNe0Vato/6oF/3r6xbVv12LzxbC8z4Bmebs8lTdMsedwrkQw17QkmPX6Lt0TpBDyeGH+P5y2b/+AW5bxm2buTJxBRUNOeoKZ/iyWaxpPyy7LUM7lYiOeIlmU5fqQyVjCe+IonROe3HBMRDNpQekxw/ixZjHKOu9LomxvfjlD4b1mW6kmnTdPob8HymV+ITKhpr1DT/nmpaTVDByY3wJPaMQcK3qpnw+szAPzc73j2v5r04JKm//znP5GMxhRWMKN6rj+C6DOf6sDvRnYC344p249RhAuhyLafk0SfNFJ/9L4x4wmmhmGH+nOhpr1CTfvnpab1GVggU3Sr4U1c0MNsVerYIZWh+rOQIAbLT86EqzLOk7NVAWM23uHP/EwQN3rEmMMFX6FiYjXjrTEv3zg4+SCoaa9Q0/6Z1zT0l99yNSekWtmYeVKfyg+2Vf/SJTg/YfmzuauHqbphTFatEi/G7OZG+nvyK1D4d2fkIUKgpr1CTftnXtPKxePh1TOaxtSi+ox5M5ZcrunxhBLPim38i5oOG2qaBM6MpnF17jCaAhyJ3RlNY2r2UxzXdW2s5rA3jVSGvkRdG6SmvwpqmgTOM01XVfVzv6tR1eqaW9M0+S0fZjU9DEN+yzHwzhi84VbT+ikE54ZxzCVfgcJz6tsPhZomgYPss6FpjO5o2xZ3lBz+PNewLMtTHENneN6hoWkYGXLHaDygR1bX+uq6XpI4HscHyIAju1LX9SVNcf4wctPGW3wF1lQco8jomJMPgpomIYO7pSE7jGDD+DkM4cA6MKAaylaWJRbiwuA1y7quq6pKjc+Dfw/aQHj9g8MwKO//97//xdARDMPoug5vMSxkXFRjEIgabYIXuvxqoRHTeIuEDOLA44a4yQdBTZOQaZ5jjFDGjSGqM9u2rVpz/IhaDFJumgbjQzBERHVXoXUoVf+gHmd89zb69WOZdl33KAqVr5iJ+ewrcAJgxuNzoaYJeY/JJ2/0fa8PnlsHOunOfXqK48k0C/kUqGlC3kPdz4LUc9d1dV2fk8TJ3dhlWZ6TxNXTR/u+v2YZ0x2fDjVNyNs8ikLdQY5EsEpM29M0zTXLnIQ6Jwn70QHwfy2qAPEy1sggAAAAAElFTkSuQmCC" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the total number of fish in the net.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find (i) the modal length interval,</span></p>
<p><span>(ii) the interval containing the median length,</span></p>
<p><span>(iii) an estimate of the mean length.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>(i) Write down an estimate for the standard deviation of the lengths.</span></p>
<p><span>(ii) How many fish (if any) have length <strong>greater than</strong> three standard deviations <strong>above</strong> the mean?</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The fishing company must pay a fine if more than 10% of the catch have lengths less than 40cm.</span></p>
<p><span>Do a calculation to decide whether the company is fined.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A sample of 15 of the fish was weighed. The weight, <em>W</em> was plotted against length, <em>L</em> as shown below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>Exactly <strong>two</strong> of the following statements about the plot could be correct. Identify the two correct statements. </span></p>
<p><span><strong>Note:</strong> You do <strong>not</strong> need to enter data in a GDC <strong>or</strong> to calculate <em>r</em> exactly.</span></p>
<p><span>(i) The value of <em>r</em>, the correlation coefficient, is approximately 0.871.</span></p>
<p><span>(ii) There is an exact linear relation between <em>W</em> and <em>L</em>.</span></p>
<p><span>(iii) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 0.012<em>L</em> + 0.008 .</span></p>
<p><span>(iv) There is negative correlation between the length and weight.</span></p>
<p><span>(v) The value of <em>r</em>, the correlation coefficient, is approximately 0.998.</span></p>
<p><span>(vi) The line of regression of <em>W</em> on <em>L</em> has equation <em>W</em> = 63.5<em>L</em> + 16.5.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>Total = 2 + 3 + 5 + 7 + 11 + 5 + 6 + 9 + 2 + 1 <em><strong>(M1)</strong></em></span></p>
<p><span><em><strong>(M1)</strong> is for a sum of frequencies.</em></span></p>
<p><span>= 51 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span>(i) modal interval is 60 – 70</span></p>
<p><span><em>Award <strong>(A0)</strong> for 65 <strong>(A1)</strong><br></em></span></p>
<p><span><br>(ii) median is length of fish no. 26, </span><span><em><strong>(M1)(A1)</strong></em></span></p>
<p><span>also 60 – 70 <em><strong>(G2)</strong></em><br></span></p>
<p><span><em>Can award <strong>(A1)</strong></em><strong>(ft)</strong><em> or <strong>(G2)</strong></em><strong>(ft)</strong><em> for 65 if <strong>(A0)</strong> was awarded </em><em>for 65 in part (i).</em></span></p>
<p><span><br>(iii) mean is \(\frac{{2 \times 25 + 3 \times 35 + 5 \times 45 + 7 \times 55 + ...}}{{51}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span><em><strong>(UP)</strong></em> = 69.5 cm (3sf) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em><br></span></p>
<p><span><em>Note: <strong>(M1)</strong> is for a sum of (frequencies multiplied by midpoint values) divided by candidate’s answer from part (a). Accept mid-points 25.5, 35.5 etc or 24.5, 34.5 etc, leading to answers 70.0 or 69.0 (3sf) respectively. Answers of 69.0, 69.5 or 70.0 (3sf) with no working can be awarded <strong>(G1).</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[5 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><em>Unit penalty <strong>(UP)</strong> is applicable where indicated in the left hand column.</em></span></p>
<p><span><em><strong>(UP)</strong></em> (i) standard deviation is 21.8 cm <em><strong>(G1)</strong></em></span></p>
<p><em><span>For any other answer without working, award <strong>(G0).</strong> If working is present then <strong>(G0)(AP)</strong> is possible.</span></em></p>
<p><br><span>(ii) </span><span>\(69.5 + 3 \times 21.8 = 134.9 > 120\)</span> <em><strong><span>(M1)</span></strong></em></p>
<p><span>no fish <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><em><span>For ‘no fish’ without working, award <strong>(G1)</strong> regardless of answer to (c)(i). Follow through from (c)(i) only if method is shown.</span></em></p>
<p><em><span> </span></em></p>
<p><em><span><strong>[3 marks]</strong><br></span></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5 fish are less than 40 cm in length, <em><strong>(M1)</strong></em></span></p>
<p><span><em>Award <strong>(M1)</strong> for any of</em> \(\frac{5}{51}\)<em>,</em> \(\frac{46}{51}\)<em>, 0.098 or 9.8%, 0.902, 90.2% or 5.1 seen.</em></span></p>
<p><span>hence no fine. <em><strong>(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><span><em>Note: There is no G mark here and <strong>(M0)(A1)</strong> is never allowed.</em></span><em> <span>The follow-through is from answer in part (a).</span></em></p>
<p><em><span><strong>[2 marks]</strong><br></span></em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) and (iii) are correct. <strong><em>(A1)(A1)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) b), c) There was much confusion about how to present the intervals. Often the mid-point only was seen. (eg. 65 instead of 60-70). Understanding of mode, median and mean was usually good but too many candidates wasted time calculating standard deviation by hand and got it wrong. In c(ii) 'greater than three' caused no problems but 'above the mean' was often ignored.</span></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) b), c) There was much confusion about how to present the intervals. Often the mid-point only was seen. (eg. 65 instead of 60-70). Understanding of mode, median and mean was usually good but too many candidates wasted time calculating standard deviation by hand and got it wrong. In c(ii) 'greater than three' caused no problems but 'above the mean' was often ignored.</span></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">a) b), c) There was much confusion about how to present the intervals. Often the mid-point only was seen. (eg. 65 instead of 60-70). Understanding of mode, median and mean was usually good but too many candidates wasted time calculating standard deviation by hand and got it wrong. In c(ii) 'greater than three' caused no problems but 'above the mean' was often ignored.</span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">d) This was often well done, even if earlier parts were poorly done.</span></p>
<p> </p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">e) Rather mixed performance here. It was hard to identify any consistency in the errors made.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Too much time was spent on this question. It was only worth two marks and candidates ought to have realised that it relied on a general pictorial understanding of the concepts, possibly supplemented by a little elementary arithmetic only, to compare (iii) and (vi). With good understanding, many of the options could be ruled out in a few seconds.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<div style="color: #3f3f3f; font: normal normal normal 14px/1.5em 'Lucida Grande', Helvetica, Arial, sans-serif; padding-top: 40px; padding-right: 10px !important; padding-bottom: 10px !important; padding-left: 10px !important; background-image: url('body-bg_1.html'); background-attachment: initial; background-origin: initial; background-clip: initial; background-color: #f7f7f7; height: 94% !important; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none; background-position: 50% 0%; background-repeat: no-repeat repeat; margin: 0px;">
<div style="color: #3f3f3f; font: normal normal normal 14px/1.5em 'Lucida Grande', Helvetica, Arial, sans-serif; padding-top: 40px; padding-right: 10px !important; padding-bottom: 10px !important; padding-left: 10px !important; background-image: url('body-bg.html'); background-attachment: initial; background-origin: initial; background-clip: initial; background-color: #f7f7f7; height: 94% !important; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px; display: inline; float: none; background-position: 50% 0%; background-repeat: no-repeat repeat; margin: 0px;">
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif;"><span style="font-size: medium; font-family: times new roman,times;">Phoebe chooses a biscuit from a blue tin on a shelf. The tin contains one chocolate biscuit and four plain biscuits. She eats the biscuit and chooses another one from the tin. The tree diagram below represents the situation with the four possible outcomes where <em style="font-style: italic;">A</em> stands for chocolate biscuit and <em style="font-style: italic;">B</em> for plain biscuit.</span></p>
<p style="margin-top: 0px; margin-right: 0px; margin-bottom: 10px; margin-left: 0px; font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; text-align: center;"><span style="font-family: times new roman,times; font-size: medium;"><img style="border-style: initial; border-color: initial; max-width: 100%; vertical-align: middle; border-width: 0px;" src="data:image/png;base64,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" alt></span></p>
</div>
</div>
</div>
<div class="specification">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">On another shelf there are two tins, one red and one green. The red tin contains three chocolate biscuits and seven plain biscuits and the green tin contains one chocolate biscuit and four plain biscuits. Andrew randomly chooses either the red or the green tin and randomly selects a biscuit.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>a</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the value of <em>b</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that both biscuits are plain.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Copy and complete</strong> the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that </span><span>he chooses a chocolate biscuit</span><span>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that he chooses a biscuit from the red tin given that it is a chocolate biscuit.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><em>a</em> = 0 \(\left( {\frac{0}{4}} \right)\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(b = \frac{3}{4}(0.75,{\text{ }}75\% )\) <strong><em>(A2)(G2)</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{4}{5} \times \frac{3}{4}\) <strong><em>(M1)(A1)</em></strong></p>
<p>\(\frac{{12}}{{20}}\left( {\frac{3}{5},{\text{ }}0.6,{\text{ 60% }}} \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for multiplying two probabilities, <strong><em>(A1)</em></strong> for using their probabilities, <strong><em>(A1)</em></strong> for answer.</p>
<p> </p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em></span></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each pair.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{1}{2} \times \frac{3}{{10}} + \frac{1}{2} \times \frac{1}{5}\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>\( = \frac{5}{{20}}\left( {\frac{1}{4},{\text{ }}0.25,{\text{ 25% }}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for two products seen with numbers from the problem, <em><strong>(M1)</strong></em> for adding two products. Follow through from their tree diagram.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]<br></span></strong></em></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{\frac{1}{2} \times \frac{3}{{10}}}}{{\frac{1}{4}}}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p><span>\( = \frac{3}{5}{\text{ }}\left( {0.6,{\text{ 60 }}\% } \right)\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></span></p>
<p><span> </span></p>
<p><strong>Note:</strong> Award <strong><em>(M1)</em></strong> for substituted conditional probability formula, <strong><em>(A1)</em></strong> for correct substitution.</p>
<p> </p>
<p>Follow through from their part (b) and part (c) (i).</p>
<p> </p>
<p><span><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">a.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 10.0px 0.0px; font: 16.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well handled by most of the candidates except for (c)(ii) in which they had to find a conditional probability. Some candidates did not copy the second tree diagram in the answer sheets and instead wrote their answers in the exam booklet thus losing the 3 marks allocated to part (b).</span></p>
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A store recorded their sales of televisions during the 2010 football World Cup. They looked at the numbers of televisions bought by gender and the size of the television screens.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">This information is shown in the table below; S represents the size of the television screen in inches.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAArYAAACfCAIAAACDXQ1sAAAgAElEQVR4nO2d3WsbWbqv9W/4SgZdyUQwm9yYuTC+CEajgDBmNzQnYHJim3GY2d3h0Lh3KLUyEwJnwCBjk0MgIErENIQ9qEs4ND0Ei8LQ9J441sVmApEKetOmLYvBHExRF0IMi7UvqiTVt0qO36o1nd9D3cRlS8qjV6t+tb6U4gAAAAAAHlJJvwAAAAAAiAgiQhxk0rM4cODAgQPHP8thXrwQEeJgpBtcLxBLAaxSAKsUwCoRiAixgjomAmIpgFUKYJUCWCUCESFWUMdEQCwFsEoBrFIAq0QgIsQK6pgIiKUAVimAVQpglQhEhFhBHRMBsRTAKgWwSgGsEoGIECuoYyIglgJYpQBWKYBVIhARYgV1TATEUgCrFMAqBbBKBCJCrKCOiYBYCmCVAlilAFaJQESIFdQxERBLAaxSAKsUwCoRiAixgjomAmIpgFUKYJUCWCUCESFWUMdEQCwFsEoBrFIAq0QgIsQK6pgIiKUAVimAVQpglQhEhFhBHRMBsRTAKgWwSsEv2uqg1/rum8p6rihrLO7nRkSIlfjqmJ2f1LYWU6lUKpVa3Ko2Owa/UOv/qV/3I9dOzln0s2REFZvoi2fnb2pbS6lUKpWaWdyqNjs61/+zrl58+AMbnb9sr95IpVKpmdXt1x3DcXZwfvJia3EmlUqlUktbtTfR/1fRrIY/u+t//eLkfBD16SPh/N9Vmx3jH7r6StWv9627PNm+nVqqdvwelZ2fNP68vTqTSqVubjUnv5uxNQJk9ebEeLO9mFmqvvdzMzg/+dZyM/Owec1vioO4I4KulrKhX5CYLV9XETJNXjYfExHhF09MdczOmg9vL27VOwbjfHTli9R+WRidZvXJts/vX55s3045uHGv/hOLdJaQaGKTfPHs/PXDxdtb9feG9c83ta2l6drNgDeFnX1b2f3+nHHOzt9UVmccbzQzTiqLzv/VzL36WbTnjGI19NnN68eM8+l/Vz+7rpQwOG/+YXHxYb2jW/88ebG1ODOz1YwchZnRaVYf7oa+C0OHPhFhcN78w2JqZnHreSNyoIynEbiGeouE+amZ8YkI7Kz5cCmVWtqqvrruXOhDAhGh+ETtmf+vvibfyaQXSlb8YoamlIqPJ0cE1t7fPYpUq2YiQUT4xRNT69CpLqU+qXb6tp/1O9WvnD8JwOg0q1uLVseDzyPfXn36xvzAj+65h01n+FlSIl3Mknzx/U71E/ejsffV39YiPX7Ym/L/T5p/G/+Qva8u2a6R7H319r2K1XEwuuH+JFIlRLIa+uy836neW618f24lVfOm1u9ycjXY++qS+/6VdWq/jfT4zOg0q1u3rdvrEIw320uLi7+e8RSD/r56bya1NLoMRySWRuDD6i0qzDipLC0u/tr7nhp/q67eSI3TGzmxR4S/No5GUdgVETjnTD/69mhCRGBGa29ZUhERwJgYI8Lt7ZNL28/6ncZfwlsHdn7SCA4H1oPU/3xi2B/lorl1c3hrEn6WlghiqV98+P1ov1P9JLVYcTwF6zQaE1rsCG+K6w/eV5dujjo/WOdVzVEGTG8+dN/oBzN1uTqfnbNOvXbieNl6c2smNc1dvt5pVh9uBzSj7H11KbO4/cb+FKzzl8aEADQ4P3kVKRxwzvnlyfbn22++ry65IoLZtXBjtfq3qfIBjzMiRKq3fqf6f7aqzY4x/YfUeLO9uvvm5PmSOyJcnmzfTs3cq76PKR/w+COCcar1Rl0j3ojA2d97fw8zyoz2/kZ2NoeIAOzEVMdm7+7iH5rR+vfY+Ul9ezWzul2fevT9orl1M7jFDz97nVxJ7HW9+Cj3o+YVZWbx4euIiq/2prCzxsOvQp6C6c2HM5Fzz7RWJz27GREiBhS906xuLd4OvXqZvdxLD5sRR04G5yf17dXF1e16tK5vZpzsrm6/Mdh7d0Tw/iQysTQCU9VbFNVeLk+2P98+uWSdqisieH8SA4lOV/SJCBaGpspSwZxJkJdqqmZwzvmgd/xswzaVwQoKhtasrOesqQzrO4faOH0iInwkxFXHzHhfW51JpWZWK6Gz0z4gHHDOzRY/uNc6/Oy1chWx1/DiI3dWcz7sl07NjIYzgh70am/K8M9C3/GL5tavo7fdU1iN9OxMbz6cmXxZneaKZXZop26MhjMCmDYcmA/+Znt198RgnkBgdsbMLG49r1fN+a1TzMSMqxGIWm+j3x9qjzJ1YBiefALBRXPrZiq1tFV9WbUmS043SfZqiBgRjHe1tYWCpGgG46z3dnc9l54rVI6tC7+ulhy9CBeqtJDbVLqMc9ZVy8VM+k5NG7Y/iAgfCTHWMTM69a3FmVToWOmHRYTBWf3zJWc3b+Sz18z0Yj/wxV/pksP1Tv3hYioVPkZ7lTdFb26NJwUGzrJkZ/V7S87O51CiWo327Jz9VL/3v5zjX65fuFI5Gu/rW0up1Mx4fq4PV3i/Bmf1/1sxX607IvQ71U+GCygY54PzN09XZ1Lujv0AYmwEItWb+0+a1a3FmxNEsZ/qD5+Z/1l3RDBdjYbGrEmsM4vETYF4EaGvyXcc6xrYaWNzPpNe2Wldcu6JCOy0sbmwLLfNeTu6Ws7ZHxAR4SMh5jpm568fLs5M7Ik1W+aZ6APe5l+d1X97r/Y+oE0MP3vtTN8lfuUXf7VwYPvz5h8WU6mJw0BXeVPMWY1BC8zYT/Xffj7V8PB0VsOfnQ/O6lv3gkbuP7A7y5o8P7Ff3Xzvbkbp9WFnjYeV4VXNHRG881QGZ/XfRZzkEW8jELXe3H8VVuS28OSNCN7pJuyn+r0bv7RFjw78IgJr14pzzqWP5q/NWTnA3Ysw/Lte61W9spGdzSAifISQ17FnRhI7q9+biTQzf7qZccbfqlvbgY1O+FkCpryYfciLnzoieCbQmZeTSIO1U09XtG5wvdcq/X31q6+ijtlbTF+uQc/OjPcvtkKmKUwdETzTb83rUKTFGhGmK9rukjmPEhGmGICnbgQ+pN5GfxJS5I7wFCUiWFVBO+YoXEQwL+qOiGD2DQxjgTcimHMR8lLt4Lh9iF6EjxLyOtbVSs3VEEw5M3+0vi5koTc7a1aeBV5Ew8/SMM2o+bW8+FEb+nLS/SjTm89rrsZx2on9Ud6U0fP5LHkdnDefVabMB/xK5er37JydNyuV5uRr/ygo/FmdNAvholl56Uy90y3WsM0j8W5pYD5UAEvVDut3qp+IGhE+sN70TvNlaAI2pxr4MrNUfc/cC1/5Rx0R7PMJrIgQ0ItgTlwoH/bY6DcRET4+6G8gqrddG+P4fGIjELh1EufsrPnVV/b+anbe3K2PJnKFniUj8u6K1/vioyyf63eq91zD86xTXZpqJyuTkDfF9th682HGUQOD8+b2lr2Hn501dyettuScX6Vcvc/O2fnrr7Ze2EZtBufNWj3kasHOTxrPJ0xXZO+rtz93bsHkc9mO8oIjbJ3ks36BndXvzThmXbBOdSnarlDEjcCV6+1q6xq82WhwVv/djENFv1P9JPqGXVdDuIjAL1uVlfGwwujXsg8a3QHnrojgygSICB8r9K3DJ47J1eZcoWtcoGwN+roYtj7hZymJJJbqxYeuazCvLrZJ3ez8+8rqjZnVa5qooTe3Zm4M7/mY0alvLdmvncOhaNftXrTIONnqhGcfzYZxPX2UC3nYFYt1qksp+ybZ5oTBq+xSEAmfJY7mhdBawcHOv6+sLkbci5O2EbhKvV0xHFhP6O0+YT/V790YrqQYnL95upq5xi01/REvInBuHO/k5zLZ9b3jHuOc9Q4f5Rc25HfuFQ3sZ/Xgv3RNXk7Pmb0IrNdqVNZz6YWS+mP74OhHxllXuZ+dzeT3WnHN7hqBiBArxHV8odb+csbMrsIbqVQqlboR2hMe2qHqc3UM6GO0Wvzws7REEEv94gPuR/Xva42fmNFpWlvVp1Iz4R3pU74p9mTjfuSgh7q+rZPCnt210sEm9UO3TmK6+rJx1jc6qkNq2HSNkO7xCO+y/y4Ieud1xXr6aWaV0jYCU9fbB2ydxDkPGmExOq+t55+JtiT4Q0koIljTC2zfzmAfWXBudTDeF8FE15RyIT1nrYq0/mntiKB3lfvZ2dzas7e9vuMpru+rHyKCiBArv+ivI0sSiKUAVimAVQpglQhEhFhBHRMBsRTAKgWwSgGsEoGIECuoYyIglgJYpQBWKYBVIhARYgV1TATEUgCrFMAqBbBKBCJCrKCOiYBYCmCVAlilAFaJQESIFdQxERBLAaxSAKsUwCoRiAixgjomAmIpgFUKYJUCWCUCESFWUMdEQCwFsEoBrFIAq0QgIsQK6pgIiKUAVimAVQpglQhEhFhBHRMBsRTAKgWwSgGsEoGIECuoYyIglgJYpQBWKYBVIgIjQsax7zQOHDhw4MCB46M7AiMCdTz5CIFVIiCWAlilAFYpgFUiEBFiBVaJgFgKYJUCWKUAVolARIgVWCUCYimAVQpglQJYJQIRIVZglQiIpQBWKYBVCmCVCESEWIFVIiCWAlilAFYpgFUiEBFiBVaJgFgKYJUCWKUAVolARIgVWCUCYimAVQpglQJYJQIRIVZglQiIpQBWKYBVCmCVCESEWIFVIiCWAlilAFYpgFUiEBFiBVaJgFgKYJUCWKUAVolARIgVWCUCYimAVQpglQJYJQIRIVZglQiIpQBWKYBVCmCViI8tIgx6re++qaznirLGEnj6X6jV5IFYCmCVAlilAFaJiCciMF0t5wK/SGpuWW7Hc71mmrxsPikighfWax283Fmbz6Rnc5Kq204Yrb3C+P1aKKkXyb1Kf8QQq2vqQUOWCr7VxXqtF1IhPZtJF0svjnvuXxj0Wl+X8nOZ9FxB+rrVG8TzisMRw2oQl63KiueDLKJGF4JaNTRVqdeklYDW+LJVWRk32tmyqifRgAYjhtVR+fl+zMPPTmwikiHOXoRBV3mQc19gdE0pLzsuSMToaimLiOCG9Q4f5ecyeal20PIUbrtWnBO5deBCiO1r8pf/Lt3N+QfQy1bl04KkaAbjrKuWVwrlQ5tnZrT2CvlyQ9M5H/TUJ4X8E1WAy5sAVoMYxlaHakE1uhDRKmvXNr8orc0H3bCNb67Ss55bCCEQwKrrVmo2k57NbSpdFuUsn9REJEacEcHsS/Dcg7L2/u4RIkJyMKO9v5Gds6rTc1ZXHy9Xjo0EXtgUiCLWjFPu6mJGa69gj1a6Wsqu7LQurX8axzv5W7bPxYUq3SoI4FwUq16M453ibwq3nKpF1ehCWKtMk5f9I8KFKq2Py1VIkrfK2rWVzT3r5n/UYXCnpvUnn53YRCSHABEhZhARXBjHO/m53Np+2ycfjLoQiiVZUTXR7hzGiCLWPyJcqNKC84cXqrQwvBUzPxejxmL4EwF6a0Sx6uayVfli5/gHp2pxNboQ1WpgRLC6EPJSTTnyu4sQgsStMu3bfccV3XG9Cz87qYlIkmQjQl87eO1oTA2tWVnPpWedQ4nWHMObkqqPfsHsThwP3sxv7P4w7pYZP85sJru+c6iN7yR8IoKuHe5tZGcz6dlMXtr3dLRfI4nXsYe+Jt/JOBpWO65JJE7JIiGKWN+IoKulrKtvtq/Jd4ZDNheqtOAavmGavJx4mBbHqgNmtJ5uVI4Nt2pxNboQ0irngRHhQpUWbOOM63uijJI7EM9qeEJ1np3QRCRJohHBON7Z3Hf0Exatrpjh0Phey/jH6CqVW6t8c9DqMdvAufJdqzfgXG/Lm7YbiAtVWrCGeVhXLRcdl0B3RLhsVe5aVz7rlwm7d4SrY9NGXqopVWsejU9IYoZ21JDNKDYnYM8tF0esX0Twa3ltySzqnySAKFbtGMc7a09bBnN7E1ijCxGtcs4n6NI1ValJxUx6lrSFvDLiWb1QpVvBtec4O6GJSJT4I4JzOcP4I93X5Ls2R6agUS+NvOyYI+O+Y3AoZqeNzYXhQ3lyiTMiME1etjUrnie6ZkSrY9NbQZLNQQTW+2FvbT6oCbCSWfZBo4spYAEgItAy6Crbe2ZxIiJcNxF0DXrqk4J7np0QiGaVdZX7xb1WwLiM6ywigonnas1OG3986fiEe5ZEWldrdz+M2fc11udb3KzXelWvbGSd6/QcEcF8GzzrMMm6dwSrY5/ZIayr3Hd3edn+QMieWy6OWEQESlj34NHusBMLEeG6iaZLlA5wF2JZZaeN339RawfcaXrOIiKYhM5FYO1a8V8Cq3PaiGDORchLtYPj9mFIL0Jfk+/EOXVRrDr2nUDqP+HOfvYWIkIggXMRXJ9/ezeYd6aSGBN7xbFqwk4b5efj2zLfuQhCanQhllUbERMV0+RlRIQw9Lb8+LEa1M/id3ZCE5EkwqxoYO1acS6w/2qqiGC8q60tDBeVhg80mIk4vp5zkeqYc99egckR4W7iwdaLKGKDVzQ4OmbMarevaHC0BaLcqIlilfMJ268VZY2Jq9GFSFYdTBEREloRFoIwVgc99fleYD4IOhveRCSJMBHB6ldx7onGfj46+m/Gp4oIrmeJMBfBPUdv0D364UeaD4AwdTyEnTY25x3JjLVrxYX7yql/Qugqn5WTr1ovoogN2BfBffVyLXrW1VJ2QcAF/aJY9cWrWlSNLoS1Gi0iDLpK+ZFgHTNcFKuDnlopye/GJce66tODYYmGnJ3URCRH4rsr2jCOd/LO6QjW/b21L9X4SsZOG5v2WXVmDrAm21tT8MqHPcZZr9WorOfSCyX1x/bB0Y/MGmvP5EdTRZwbi6ZnM+n5oAvkhyNGHTtgXeV+driakfXe7q7fHHvuqn8sD5eMMkNTHklf+2+fkDSiiA3qg7Fvl2a0G5Jr6zT7VoC6ppQF2RZQFKu++KgWVKMLYa0GzOg6fCw9bVp7ouia8ifHRU4YBLBqzeX0n0434ezEJiIx4okI3k5C/6AwvKKbSxz3mpru/ttsWf35sJS1P87PjimHRVljuqaUC8MdEXRz/t3as7e9vvuhzMjGei2lYu2L4NpE4boRoI69MEN7bX41QyZdLMmqbXcUczWptWOEz97MwiCAWFeRe+7GWO/trlnbAd/RcPxsIzsr1JcLCGA1GP80JqJGF0JadW5+YJ8lZ7yrWY3DXEGqvhK1DUjaatBAmHmlCz87eozwJiIZ4uxFALBKBcRSAKsUwCoFsEoEIkKswCoREEsBrFIAqxTAKhGICLECq0RALAWwSgGsUgCrRCAixAqsEgGxFMAqBbBKAawSgYgQK7BKBMRSAKsUwCoFsEoEIkKswCoREEsBrFIAqxTAKhGICLECq0RALAWwSgGsUgCrRCAixAqsEgGxFMAqBbBKAawSgYgQK7BKBMRSAKsUwCoFsEoEIkKswCoREEsBrFIAqxTAKhGICLECq0RALAWwSgGsUgCrRIRFBBw4cODAgQPHx3wERgTqePIRAqtEQCwFsEoBrFIAq0QgIsQKrBIBsRTAKgWwSgGsEoGIECuwSgTEUgCrFMAqBbBKBCJCrMAqERBLAaxSAKsUwCoRiAixAqtEQCwFsEoBrFIAq0QgIsQKrBIBsRTAKgWwSgGsEoGIECuwSgTEUgCrFMAqBbBKBCJCrMAqERBLAaxSAKsUwCoRiAixAqtEQCwFsEoBrFIAq0QgIsQKrBIBsRTAKgWwSgGsEoGIECuwSgTEUgCrFMAqBbBKBCJCrMAqERBLAaxSAKsUwCoR/7wRYdBrffdNZT1XlDWW9GuJjPBW/1mBWApglQJYpQBWiYgnIjBdLeesr42aW5bbgdd0XS1lI/wa50yTl80HRET4QFiv9UIqmDLz0n6r59Y5/oVi6cWx57QQiCjWYphl07OZbFnVR/qY0dorjL9ObaGkXiT5Mv0QwyoztKOGUi3l79a0fvCvXbYqK57WYNBrfV3Kz2XScwXp61ZvQP1aoyCGVS+XrcrK+Pv9HLU68WzyiGF1VG++rSUztNc7a/PmBa4gyaqmO/5ayJY2zl6EYZEFlldfk+9McdU38wQiwgfh/OSnZzPp+fvKKXP8wqcFSdEMxllXLa8UyoeC1K4d8cRyzjlnXbVczKSLJflb9/WJtWvFOZHbXC6GVabt3//yy43sbCZ9JzgiDPOWozVgRmuvkC83NJ3zQU99Usg/UQVICSJY9TK+6UrPZtKzOUnVI58VAQGsukL/bCY9m9tUusOCZF3lfrZYUtoG55zrmlIuZB80uqOCFLSljTMi9DV583+vfZoL6iHQ1VLx7kZ+Lmr9ISJ8MEyT/3Xt2Vuz3Rxl2LFSZrT2Cvarl66Wsis7rcuEXm8goonlnHPjXW1tPmNdolwwXX28XDk2EnhZUyCMVfPmITgiGMc7xd8Ubs05WgPjeCd/y9Y3c6FKtwoCOBfGqp0LVVoP/lyHnxWC5K2ydm1lc8+6+R91J4yK9kKVFhz1ydq14r8ML4XitrQxR4R/Kx0e1YpzfvdM47OICHHR15R6y7Dru1ClBdu74ylrfqFKC7iHiMBlq7KSyW7W2n6qrC6EYklW3J2NIiGM1fCIcNmqfLFz/EOtaI8I5uCm/U+YrpZzAvTWCGN1jNVJkJdqypFmuP2EnxWExK0y7dt9xxXdrMDRAGJfk+84LnysXSt+OgwB4ra0sUcEtdtVHuTcvdmcG8c7m/vaP9ruiGBoTXMcNz2bya7vHGrjmwCfiKBrh3sb2eBh9aRJvI4n4axLXS1lXZ2KnkIXA9HEMk1eDpxPY5+aM5tJz2/s/iBcpXLOBbIaEhGY0Xq6UTk2zNQ1bg1cYZdz601Jfs6HMFZHXKjSgm3Ma33PMQ4eflYUxLPqjqSsq9zPzg67FfW2/MV9+Z11ORO4pY0/Ilxw43gnP5fJ79nuXwddpfxIvTDvrmymLlRpwRrOsYZ1bc2EOyJctip3rdbW+mUhOmrsiFfHTnS1lB0b9rvOTeryTQjBxJqtarEk/0dNKgbPXTpqyObspDkROsC9CGM1uOqM4521py2DcVdEcCcGzifktvgQxqoLXVOVYbl6W87ws8kjntULVbrlLDZmtPc3srOZ9G82pIr9DlbkljaJiMAH7o4E5+d8HBHYaWNzYTRa4+y3cUcEpsnLthbB7BwToaPGjnh1bGfQVb6wD5CLXLguxBJrXp/yUk3VDM45673dXc8F5ADWO3yUn8s4Ji6JgjBWg6pu0FW298zLFSLC9TDoqU8Kznl2kc8miWhWWVe5X9xrucdlzGufuaJBGY3aiNzSJhIRXFf3QVeRPjPjgrsXwYL1Wq/qlY2sc22Y40GGqyFchwAdNXZEq2M7rKt8trnfttW0yIXrQiyx3m5DdtrYnA+qRkE6wL0IY9W/6lj34NHuMHUhIlwb4V3conSAuxDLKjtt/P4LzzwkvS1/8Zlyyqx7htncmtXeitzSJhQRrP//QskcXNh8aqUtb0Qw5yLkpdrBcfswpBehr8l3xJ+6KFYd2zHe1aSKe0mYrpayrsL1GeIVAbHEBo0sBn3gWbtWvIWIEIyfPXbaKD8f36X5zkVwroF0d0MmhDBWA2GavBz8GQ8/mxQiWdXb8uPHqqufxTU1QdeUcmEUCwRuaZOKCKMLfPXt4Z8+G404uCKC8a62tjBcHho+0GBmWxF7a+2IVMc2WFfdfe63ZNwzqzagmydxxBLrY2liRAjfFygZhLHqteea8uk8irLGvOsXRLn9FcZqIK5B26nOJoUwVgc99fmeOx/4dmvZU6y4LW1yEWE0NOBeBzLy4soEEeYiuBcyDLpHP/woUikLU8c2WFf942N7nxjrqf9P0cbzP4RcretCMLGDrvIg5wisfU2+EzSCy7rKZ+Xk2wIvwliN0OnqbYJ1tZRdwL4I0zOcPH6Vs4khhtVBT62URusUOOesqz49GIUA5yT9vibfcVzshGxpE4wIfr0r5mIHx1V/zuxFYL1Wo7KeSy+U1B/bB0c/stEakpH0iRsFJo8YdWzDWvrhug+zNaz2fb6MdkMSZc8vF+KJPW1szuesbakGveNnG78aJgbWVf9YHi7fZYamPJK+bgu53FwYq1eKCI4dFXVNKWN3RV9Y7/Cx9LRp7c+ha8qf7Be58LPiIIBVay6nqzkdhQCjtVcYXs6s1Q2/su2bImpLG09EcPUKjj7ql63dZ45desa/Y0YHc8DG2hFB7yr3s7O5tWdve33HA47CF+u1lIq1L4JrEwUxEKCO7bicB8zxHE6uEWrncBeCieWc27f0cO3HrrflzdzwSzFqB+Jt3zFECKvj720J/U4Wv/mJVjjLzuI7GsIwtwG1CrX6ylWP4WeFIWmrQSNf9n6sQa+lhH9Hg4AtbZy9CABWqYBYCmCVAlilAFaJQESIFVglAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglQhEhFiBVSIglgJYpQBWKYBVIhARYgVWiYBYCmCVAlilAFaJQESIFVglAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglQhEhFiBVSIglgJYpQBWKYBVIhARYgVWiYBYCmCVAlilAFaJQESIFVglAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglYiwiIADBw4cOHDg+JiPwIhAHU8+QmCVCIilAFYpgFUKYJUIRIRYgVUiIJYCWKUAVimAVSIQEWIFVomAWApglQJYpQBWiUBEiBVYJQJiKYBVCmCVAlglAhEhVmCVCIilAFYpgFUKYJUIRIRYgVUiIJYCWKUAVimAVSIQEWIFVomAWApglQJYpQBWiUBEiBVYJQJiKYBVCmCVAlglAhEhVmCVCIilAFYpgFUKYJUIRIRYgVUiIJYCWKUAVimAVSIQEWIFVomAWApglQJYpQBWiUBEiBVYJQJiKYBVCmCVAlgl4pcYEVivdfByZ21hWW6zpF+Li39iq2IDsRTAKgWwSgGsEhFXRNDVUjb066SyZVW/lgt6X5PvZNKzmfQcIkI0dO1wb8N6d4olWdUMlzZmtPYK4zdroaReJPNKgxFDrK6pBw1ZKhRlLbDyBr3Wd0cwhK0AAAfxSURBVN9U1nPemjeOd/Jzo09ETlL1OF5zGGJYZYZ21FCqpfzdmtZ3nzS0pikzPZvJSzVVMxynB73W16X8XCY9V5C+bvUGsb3oEMSwamfUZjoOewWy3vG+VDQl77d6orWrXCCroa0l67VeSAWzpX1x7PYYfjYhYowIxSeq9RE1K3LkjhmaUio+nhwRWHt/9yhCu8l0tZxDRIjEoKs8yOXLDU3nnHOj3ZCKuU2laxfH2rXiHEGYu04EENvX5C//XbqbS89mgiIC66rlYiZdLMnfei5XrmZaiBwmgFXOtP37X365kZ3NpO+4IwI7bWwuFCRFM5jVjOQX7iunQ/fMaO0VrNoe9NQnhfyoCUoSEaw6cH3ArcNm2zjeya+UlLbBOesdPsqvPFK7ojUBolgNay0vW5VPrXJlXbW8Uigf2nJA+NnEiC0i/LVxNGryXBGBc870o2+PJlx4mNHaW450a4WIEBldLWUdopgmLzvaYqarj5crx4b/34uCKGLNBsI3IhjvamvzmVEac6GrpeJey91/kzCiWLVaDFdEMD/m9h/2NfnOWL5xvJO/ZWtkLlTpVkGAShbGqgXTXj7a/cFxNdLV0sqohi9blRVbjwLT1XIuj1r1JaS1ZEZrr2BPDLpayq7stC4jnE2SuCKCcaqN87s3InD2997fw0qOGe39jWzE3ldEhMiwdq045+hR1ORl++ffCsXFkqyovtc2MRBFbGBEuGxVVjLZzVrb16H5iZgrSNWGu6s8SUSx6h8RzDhrb0b6mnx3GAK8AYLpajknQB+YMFZNmPHjj867Vaarj/911Hh67iK4rpayQvRy2RHCalhreaFKC86W4UKVFoZtb/jZJElkuqJPROCcc84MTa2ZI17puYIkDy0PesfPNrKuQTJmaK931uatn6ztNcdvCSJCdAZd5UEuPWd1cBnvaptf2C5jpsmR+fkN192GMIgiNiAiME1eDilI50yd3NqztwL0h3NxrAZEBM5OG5vzmXSxpLQNzoz2/v3N/baVbi9UacE1KOaJFMkgjNUgLlTp34aqzRbANaDuvq8QAQGshraWulpy3+L2NfmOVaLhZxNFnIhg9hMUhyNeP+ytzWfStp4Wl0RdLWXnzXFH1jt8lLe3y4gIU6G35c1cejaTXy9VXvpN6WKGdtSQzXk0cyJ01XoRRax/RLhQpYVMuliS/2OYgP2mIxmaqlRL5oxFMTpyRbEaFBH4cPgmPVdYk3bsSv3eiAlBLS6EsRqAY5TBz3zIaFpyCGPVv7X0q72x2/CzMf8HXAgTEbw93l3lftbWVjojAusq97Mjfa47BkSEKbHuxmaHN2QBv2VGseyDRleIe1w7ooj1bT3NH47m27Pe2931XFDYsqY0ztum3SWGKFZDm0uroUjPOuZ5ICJcEecoAyLCVXG1logIU+E3F0GTl10LvaxxnaEjn64YHrCEDBFhGox3tU2p0R0Me27mN+R3gSlBjK5aL6KI9W09vaVrZrKgXkRhOnJFsRrYXDKjvX//90qXDcciR7M9EBGuiH2UgSMifAj21hIRYSr8VjSo5Zx7LbjZPTv8NXc7a85FWChI1Vet/2qiF+GKOCfFGO2GVAyrS9auFW8hIgQSMSJM+Pz3NfkOIoKNAF2OeXPmoseRfO/8L79h9SQQxqofjlEG7jfrM+huLWFEtGpvLb2zPu2d3+FnE0WsiOCd0hnQi2BNXBguz8VAwxXxSa8+xWr/g3at6LeDTdKIIjZ4oGHKiHBXhOoVxaq/Lu8P7dcz7/oF4eZ/iYdrlIFz7rN+QcyuRBGtOlpLzwoFR7MQfjZJBIkIo63lbB9409FoGx9HRHBlAkSEq6KrpaxzUDy0n4B1lc/KyVetF1HE+vfBDrrKg5xjDkdfk++4t6gaP8hp4/d/SvxKxsWxGrYvgmPtONPk5VE74L62YV+EibhGGUY/XMC+CFfA2Vp6MqtzX4TQs0kiTEQY7ls5XPE16KlPCvZ15KOIwH5WD/7aku9k0mYvwqDXUnbW5jPZstp990r9bzZayCdAc+BCvDq+bFVWhia5ubrh5tpw5Rjrqn8s7xyaK/WZoSmPpK/bgjUNJqKIDRqmZaeNzflxbR8/2/jVKDEMemqlVHlt7XtttBvlxwHbJ8SNKFaDOl3M+4rRnonGu9rab2wzaew7KuqaUsbuihNwjzJY2HZUNEdzsLuiHxNbS/ueiUa7ITn3Tww/mxwxRwTXylHXpqr2rQ7s+yKY6JpSLoxX8Juj5uaOCBdd5UHOWodqDk8ItNG9neTr2AvrtZRKwHc0DNdDmhvgHwi5OTvnXAixrtr2dGKNv03AVdvWtmBD/969mRNDAKuer3dxzUDstRrh39FgbamC72iYiN8ow+icNZcZ39EQQoTW0lrNFPgdDWFnEyKRXoSPF1glAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglQhEhFiBVSIglgJYpQBWKYBVIhARYgVWiYBYCmCVAlilAFaJQESIFVglAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglQhEhFiBVSIglgJYpQBWKYBVIhARYgVWiYBYCmCVAlilAFaJQESIFVglAmIpgFUKYJUCWCUCESFWYJUIiKUAVimAVQpglQhEhFiBVSIglgJYpQBWKYBVIsIiAg4cOHDgwIHjYz78IwIAAAAAAEdEAAAAAIAviAgAAAAA8AERAQAAAAA+/A9yjcDngTvgxwAAAABJRU5ErkJggg==" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">The store wants to use this information to predict the probability of selling these sizes of televisions for the 2014 football World Cup.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use the table to find the probability that</span></p>
<p><span>(i) a television will be bought by a female;</span></p>
<p><span>(ii) a television with a screen size of 32 < <em>S</em> ≤ 46 will be bought;</span></p>
<p><span>(iii) a television with a screen size of 32 < <em>S</em> ≤ 46 will be bought by a female;</span></p>
<p><span>(iv) a television with a screen size greater than 46 inches will be bought, given that it is bought by a male.</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong></strong>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></p>
<p><span>Write down the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Show that the expected frequency for females who bought a screen size of 32 < <em>S</em> ≤ 46, is 79, correct to the nearest integer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the \({\chi ^2}\) calculated value.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>The manager of the store wants to determine whether the screen size is independent of gender. A Chi-squared test is performed at the 1 % significance level.</span></span></p>
<p><span>Determine if the null hypothesis should be accepted. Give a reason for your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{220}}{{500}}\left( {\frac{{11}}{{25}},{\text{ 0}}{\text{.44, 44}}\% } \right)\) <em><strong>(A1)(G1)</strong></em></span></p>
<p> </p>
<p><span>(ii) \(\frac{{180}}{{500}}\left( {\frac{{9}}{{25}},{\text{ 0}}{\text{.36, 36}}\% } \right)\) <em><strong>(A1)(G1)</strong></em></span></p>
<p> </p>
<p><span>(iii) \(\frac{{40}}{{500}}\left( {\frac{{2}}{{25}},{\text{ 0}}{\text{.08, 8}}\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p> </p>
<p><span>(iv) \(\frac{{55}}{{500}}\left( {\frac{{11}}{{56}},{\text{ 0}}{\text{.196, 19.6}}\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p> </p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator. Award <em><strong>(A0)(A0)</strong></em> if answers are given as incorrect reduced fractions without working.</span></p>
<p> </p>
<p><em><strong><span>[6 marks]</span></strong></em></p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>“The size of the television screen is independent of gender.” <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept “not associated”, do not accept “not correlated”.</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<p> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{180}}{{500}} \times \frac{{220}}{{500}} \times 500\) <strong>OR</strong> \(\frac{{180 \times 220}}{{500}}\) <em><strong>(M1)</strong></em></span></p>
<p><span>= 79.2 <em><strong>(A1)</strong></em></span></p>
<p><span>= 79 <em><strong>(AG)</strong></em> </span></p>
<p><span><strong>Note:</strong> Both the unrounded and the given answer must be seen for the final <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\chi _{calc}^2\) = 104(103.957...) <em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> if an attempt at using the formula is seen but incorrect answer obtained.</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>11.345 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Follow through from their degrees of freedom.</span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\chi _{calc}^2\) > \(\chi _{crit}^2\) <strong>OR</strong> <em>p</em> < 0.01 <strong><em>(R1)</em></strong></span></p>
<p><span>Do not accept H<sub>0</sub>. <strong><em>(A1)</em>(ft)</strong> </span></p>
<p><span><strong>Note:</strong> Do not award <em><strong>(R0)(A1)</strong></em><strong>(ft)</strong>. Follow through from their parts (d), (e) and (f).</span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Part (a) was generally well answered by most of the students, except for part (a)(iv) which called for conditional probability. </span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students correctly stated the null hypothesis in part (b), and answered parts (d), (e), (f) and (g). </span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In some responses to part (c) it seemed that the difference between calculation of the expected value and showing that the value is 79 was not clear to the candidates. It is important that teachers explain to their students that in a <em><strong>“show that”</strong> question</em> they are expected to demonstrate the mathematical reasoning through which the given answer is obtained.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students correctly stated the null hypothesis in part (b), and answered parts (d), (e), (f) and (g). </span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students correctly stated the null hypothesis in part (b), and answered parts (d), (e), (f) and (g). </span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students correctly stated the null hypothesis in part (b), and answered parts (d), (e), (f) and (g). </span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most students correctly stated the null hypothesis in part (b), and answered parts (d), (e), (f) and (g). </span></p>
<div class="question_part_label">g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A group of 50 students completed a questionnaire for a Mathematical Studies project. The following data was collected.</span></p>
<p style="margin-left: 60px;"><span style="font-family: times new roman,times; font-size: medium;">\(18\) students own a digital camera (D)</span><br><span style="font-family: times new roman,times; font-size: medium;">\(15\) students own an iPod (I)</span><br><span style="font-family: times new roman,times; font-size: medium;">\(26\) students own a cell phone (C)</span><br><span style="font-family: times new roman,times; font-size: medium;">\(1\) student owns all three items</span><br><span style="font-family: times new roman,times; font-size: medium;">\(5\) students own a digital camera and an iPod but not a cell phone</span><br><span style="font-family: times new roman,times; font-size: medium;">\(2\) students own a cell phone and an iPod but not a digital camera</span><br><span style="font-family: times new roman,times; font-size: medium;">\(3\) students own a cell phone and a digital camera but not an iPod</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Claire and Kate both wish to go to the cinema but one of them has to stay at home to baby-sit.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The probability that Kate goes to the cinema is \(0.2\). If Kate does not go Claire goes.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If Kate goes to the cinema the probability that she is late home is \(0.3\).</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">If Claire goes to the cinema the probability that she is late home is \(0.6\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Represent this information on a Venn diagram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the number of students who own none of the items mentioned above.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If a student is chosen at random, write down the probability that the student owns a digital camera <strong>only</strong>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><span>If two students are chosen at random, calculate the probability that they both own a cell phone</span> <span><strong>only</strong>.</span></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>If a student owns an iPod, write down the probability that the student also owns a digital camera.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Copy and complete the probability tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Calculate the probability that</span></p>
<p><span>(i) Kate goes to the cinema and is not late;</span></p>
<p><span>(ii) the person who goes to the cinema arrives home late.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">ii.b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)(A1)</strong></em><strong>(ft) </strong></span></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for rectangle with 3 intersecting circles, <em><strong>(A1)</strong></em> for \(1\), <em><strong>(A1)</strong></em> for \(5\), \(3\), \(2\), <strong><em>(A1)</em>(ft)</strong> for \(9\), \(7\), \(20\) if subtraction is carried out, or \(18\), \(15\), \(26\) seen by the letters D, I and C.</span></p>
<p><span><em><strong>[4 marks]</strong></em><br></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(50 - 47\) <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for subtracting their value from \(50\).</span></p>
<p><br><span>\( = 3\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><span><strong><em>[2 marks]<br></em></strong></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{9}{{50}}\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong><em>[1 mark]</em><br></strong></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{20}}{{50}} \times \frac{{19}}{{49}}\) <em><strong>(A1)</strong></em><strong>(ft)<em>(M1)</em></strong></span></p>
<p><span>\( = \frac{{38}}{{245}}{\text{ }}\left( {\frac{{380}}{{2450}}{\text{, }}0.155{\text{, }}15.5\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><br><span><strong>Notes: <em>(A1)</em>(ft)</strong> for correct fractions from their Venn diagram</span><br><span><em><strong>(M1)</strong></em> for multiplying their fractions</span><br><span><em><strong>(A1)</strong></em><strong>(ft)</strong> for correct answer.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{6}{{15}}{\text{ }}\left( {\frac{2}{5}{\text{, }}0.4{\text{, }}40\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)<em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note: <em>(A1)</em>(ft)</strong> for numerator, <strong><em>(A1)</em>(ft)</strong> denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em></span></span></p>
<p><span><strong>Note:</strong> <em><strong>(A1)</strong></em> for \(0.8\), <em><strong>(A1)</strong></em> for \(0.7\), <em><strong>(A1)</strong></em> for \(0.6\) and \(0.4\).<em><strong><br></strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(0.2 \times 0.7 = 0.14\) <em><strong>(M1)(A1)</strong></em><strong>(ft)<em>(G2)</em></strong></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for multiplying correct numbers.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<p><span><br>(ii) \(0.2 \times 0.3 + 0.8 \times 0.6\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><span>\( = 0.54\) <em><strong>(A1)</strong></em><strong>(</strong><strong>ft)<em>(G3)</em></strong></span></p>
<p><br><span><strong>Note: <em>(M1)</em></strong> for each correct product (use candidate’s tree), <em><strong>(A1)</strong></em><strong>(ft)</strong> for answer.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The Venn diagram was well drawn on the whole although some of the candidates missed out the Universal box and others filled in the intersections wrongly but still gained ft marks for the remaining parts of the question.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Well answered.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Well answered.</span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Few correct answers. Either candidates added instead of multiplying or they used replacement and so the fractions given were the same.</span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Again few correct answers. Candidates wrote the answer out of \(50\) instead of \(15\).</span></p>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The tree diagram was well done on the whole. It appears as if some candidates may have completed this on the exam paper and this was not included with their papers. However, the question did state clearly “Copy and complete …”</span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) This part was well done by those candidates who remembered to multiply instead of add.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(ii) Many candidates just wrote down “Claire” for this answer. Others wrongly multiplied or added \(0.3\) with \(0.6\).</span></p>
<div class="question_part_label">ii.b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">One day the numbers of customers at three cafés, “Alan’s Diner” ( \(A\) ), “Sarah’s Snackbar” ( \(S\) ) and “Pete’s Eats” ( \(P\) ), were recorded and are given below.</span></p>
<p><br><span style="font-family: times new roman,times; font-size: medium;"> 17 were customers of Pete’s Eats only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 27 were customers of Sarah’s Snackbar only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 15 were customers of Alan’s Diner only</span><br><span style="font-family: times new roman,times; font-size: medium;"> 10 were customers of Pete’s Eats <strong>and</strong> Sarah’s Snackbar <strong>but not</strong> Alan’s Diner</span><br><span style="font-family: times new roman,times; font-size: medium;"> 8 were customers of Pete’s Eats <strong>and</strong> Alan’s Diner <strong>but not</strong> Sarah’s Snackbar</span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">Some of the customers in each café were given survey forms to complete to find out if they were satisfied with the standard of service they received.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Draw a Venn Diagram, using sets labelled \(A\) , \(S\) and \(P\) , that shows this information.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 48 customers of Pete’s Eats that day. Calculate the number of people who were customers of all three cafés.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There were 50 customers of Sarah’s Snackbar that day. Calculate the total number of people who were customers of Alan’s Diner.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of customers of Alan’s Diner that were also customers of Pete’s Eats.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(n[(S \cup P) \cap A']\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Dissatisfied”;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Satisfied” and was completed at Sarah’s Snackbar;</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the survey forms was chosen at random, find the probability that the form showed “Dissatisfied”, given that it was completed at Alan’s Diner.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span> Write down the null hypothesis, \({{\text{H}}_0}\) , for the \({\chi ^2}\) test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>Write down the number of degrees of freedom for the test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>Using your graphic display calculator, find \({\chi ^2}_{calc}\) .<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>A \({\chi ^2}\) test at the \(5\% \) significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés.</span></p>
<p><span>State, giving a reason, the conclusion to the test.<br></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.g.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for rectangle and three labelled intersecting circles</span><br><span><em><strong>(A1)</strong></em> for \(15\), \(27\) and \(17\)</span><br><span><em><strong>(A1)</strong></em> for \(10\) and \(8\) <em><strong>(A3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(48 - (8 +10 +17)\) <em>or equivalent</em> <em><strong>(M1)</strong></em></span></p>
<p><span>\( = 13\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(50 - (27 +10 +13)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for working seen.</span></p>
<p> </p>
<p><span>\( = 0\) <em><strong>(A1)</strong></em></span><br><span>number of elements in A \(= 36\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G3)</strong></em></span></p>
<p><span><strong>Note:</strong> Follow through from (b).</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(21\) <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from (b) even if no working seen.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(54\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(17\), \(10\), \(27\) seen. Follow through from (a).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{40}}{{120}}{\text{ }}\left( {\frac{1}{3}{\text{, }}0.333{\text{, }}33.3\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{34}}{{120}}{\text{ }}\left( {\frac{{17}}{{60}}{\text{, }}0.283{\text{, }}28.3\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{8}{{28}}{\text{ }}\left( {\frac{2}{7}{\text{, }}0.286{\text{, }}28.6\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for numerator, <em><strong>(A1)</strong></em> for denominator.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>customer satisfaction is <strong>independent</strong> of café <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept “customer satisfaction is <strong>not associated with</strong> the café”.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<p><span> </span></p>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(2\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.754\) <em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(G1)(G1)(AP)</strong></em> for \(0.75\) or for correct answer incorrectly rounded to 3 s.f. or more, <em><strong>(G0)</strong></em> for \(0.7\).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>since \({\chi ^2}_{calc} < {\chi ^2}_{crit}5.991 accept (or Do not reject) H<sub>0</sub> <strong><em>(R1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from their value in (e).</span></p>
<p><span><strong>OR</strong></span></p>
<p><span>Accept (or Do not reject) H<sub>0</sub> as \(p\)-value \((0.686) > 0.05\) <strong><em>(R1)(A1)</em>(ft)</strong></span></p>
<p><span><strong>Notes:</strong> Do not award <em><strong>(A1)(R0)</strong></em>. Award the <em><strong>(R1)</strong></em> for comparison of appropriate values.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.g.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. A common mistake was the failure to intersect all three sets.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. A common mistake was the failure to intersect all three sets.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. A common mistake was the failure to intersect all three sets.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. A common mistake was the failure to intersect all three sets.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part A</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. A common mistake was the failure to intersect all three sets.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A surprising number seemed unfamiliar with set notation in (e) and thus did not attempt this part.</span></p>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"> </span></p>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The chi-squared test was well done by the great majority, however, it was clear that a number of centres do not teach this subject, since there were a number of scripts which either were left blank or showed no understanding in the responses seen.</span></p>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The chi-squared test was well done by the great majority, however, it was clear that a number of centres do not teach this subject, since there were a number of scripts which either were left blank or showed no understanding in the responses seen.</span></p>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The chi-squared test was well done by the great majority, however, it was clear that a number of centres do not teach this subject, since there were a number of scripts which either were left blank or showed no understanding in the responses seen.</span></p>
<div class="question_part_label">B.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><strong>Part B</strong></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The work on probability also proved accessible to the great majority with a large number of candidates attaining full marks. Most errors occurred due to candidates trying to use the algebraic form of laws of probability, rather than by interpreting the contingency table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">The chi-squared test was well done by the great majority, however, it was clear that a number of centres do not teach this subject, since there were a number of scripts which either were left blank or showed no understanding in the responses seen.</span></p>
<div class="question_part_label">B.g.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The Venn diagram below represents the students studying Mathematics (<em>A</em>), Further Mathematics (<em>B</em>) and Physics (<em>C</em>) in a school.</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">50 students study Mathematics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">38 study Physics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">20 study Mathematics and Physics but not Further Mathematics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">10 study Further Mathematics but not Physics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">12 study Further Mathematics and Physics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">6 study Physics but not Mathematics</span></p>
<p style="margin-left: 30px;"><span style="font-size: medium; font-family: times new roman,times;">3 study none of these three subjects.</span></p>
<p style="text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Three propositions are given as</span></p>
<p style="margin-left: 30px; text-align: center;"><span style="font-size: medium; font-family: times new roman,times;"><em>p</em> : It is snowing <em>q</em> : The roads are open <em>r</em> : We will go skiing</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Copy and complete the Venn diagram <strong>on your answer paper</strong>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of students who study Mathematics but not Further Mathematics.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the total number of students in the school.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n({\text{B}} \cup {\text{C}})\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound statement in symbolic form.</span></p>
<p><span>“It is snowing and the roads are not open.”</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write the following compound statement in words.</span></p>
<p><span>\((\neg p \wedge q) \Rightarrow r\)</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>An incomplete truth table for the compound proposition \((\neg p \wedge q) \Rightarrow r\) is given below.</span></p>
<p><span>Copy and complete the truth table<strong> on your answer paper</strong>.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">B, c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em></span> </span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct number in the correct position.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>28 <em><strong>(A1)</strong></em><strong>(ft)</strong> </span></p>
<p><br><span><strong>Note:</strong> 20 + their 8.</span></p>
<p><span> </span></p>
<p><em><strong><span>[1 mark]</span></strong></em></p>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>59 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span><strong>[1 mark]</strong></span></em></p>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>10 + 12 + 20 + 6 <em><strong>(M1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for use of the correct regions.</span></p>
<p><br><span>= 48 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><strong><span>OR</span></strong></p>
<p><span>59 − 8 </span><span><span>−</span> 3 <em><strong>(M1)</strong></em></span></p>
<p><span>= 48 <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span><strong>[2 marks]</strong></span></em></p>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p \wedge \neg q\) <em><strong>(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(\wedge\), <em><strong>(A1)</strong></em> for both statements in the correct order.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>If it is not snowing and the roads are open (then) we will go skiing. <em><strong>(A1)(A1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for “if…(then)”, <em><strong>(A1)</strong></em> for “not snowing and the roads are open”,</span> <span><em><strong>(A1)</strong></em> for “we will go skiing”.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt><span> <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct column.</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">B, c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.</span></p>
<div class="question_part_label">A, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.</span></p>
<div class="question_part_label">A, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.</span></p>
<div class="question_part_label">A, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This part was successfully attempted by the great majority. The less familiar form of the Venn diagram seemed not to cause too many problems, although a common mistake was the failure to add the 20 in set A in part (b). A surprising number seemed unfamiliar with set notation in (d) and thus were not able to attempt this part.</span></p>
<div class="question_part_label">A, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).</span></p>
<div class="question_part_label">B, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).</span></p>
<div class="question_part_label">B, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The work on logic also proved accessible to the great majority with a large number of candidates attaining full marks. The most common errors were the omission of the “If” in the conditional statement in (b) and the inability to follow the implication in the truth table in (c).</span></p>
<div class="question_part_label">B, c.</div>
</div>
<br><hr><br><div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part A</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">100 students are asked what they had for breakfast on a particular morning.</span> <span style="font-family: times new roman,times; font-size: medium;">There were three choices: cereal (<em>X</em>) , bread (<em>Y</em>) and fruit (<em>Z</em>). It is found that</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">10 students had all three</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">17 students had bread and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">15 students had cereal and fruit only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">12 students had cereal and bread only</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">13 students had only bread</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">8 students had only cereal</span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;">9 students had only fruit</span></p>
</div>
<div class="specification">
<h1><span style="font-family: times new roman,times; font-size: medium;">Part B</span></h1>
<p><span style="font-family: times new roman,times; font-size: medium;">The same 100 students are also asked how many meals on average they have per day. The data collected is organized in the following table.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img 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" alt></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">A \({\chi ^2}\) test is carried out at the 5 % level of significance.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Represent this information on a Venn diagram.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the number of students who had none of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the percentage of students who had fruit for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Describe in words what the students in the set \(X \cap Y'\) had for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that a student had <strong>at least</strong> two of the three choices for breakfast.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random. Find the probability that both students had all three choices for breakfast.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">A.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis, H<sub>0</sub>, for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Show that the expected number of females that have more than 5 meals per day is 13, correct to the nearest integer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to find the \(\chi _{calc}^2\) for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Decide whether H<sub>0</sub> must be accepted. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">B.f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt></span></p>
<p><span><em><strong>(A1)</strong></em> for rectangle and three intersecting circles</span></p>
<p><span><em><strong>(A1)</strong></em> for 10, <em><strong>(A1)</strong></em> for 8, 13 and 9, <em><strong>(A1)</strong></em> for 12, 15 and 17 <em><strong>(A4)</strong></em></span></p>
<p><span><em><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>100 – (9 +12 +13 +15 +10 +17 + 8) =16 <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><span><strong>Note:</strong> Follow through from their diagram.</span></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{51}}{{100}}(0.51)\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span>= 51% <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Follow through from their diagram.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><strong>Note:</strong> The following statements are correct. Please note that the connectives are important. It is not the same (had cereal) <span>and</span></span> <span>(not bread) and (had cereal) <span>or</span> (not bread). The parentheses are not needed but are there to facilitate the understanding of </span><span>the propositions.</span></p>
<p><span> </span></p>
<p><span>(had cereal) and (did not have bread)</span></p>
<p><span>(had cereal only) or (had cereal and fruit only)</span></p>
<p><span>(had either cereal or (fruit and cereal)) and (did not have bread) <em><strong>(A1)(A1)</strong></em> <br></span></p>
<p><br><span><strong>Notes:</strong> If the statements are correct but the connectives are wrong then</span> <span>award at most <strong><em>(A1)(A0)</em></strong>.</span> <span>For the statement (had only cereal) and (cereal and fruit) award </span><em><strong><span>(A1)(A0)</span></strong></em><span>. </span><span>For the statement had cereal and fruit award <em><strong>(A0)(A0)</strong></em>.</span></p>
<p><em><strong>[2 marks]</strong></em></p>
<p> </p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{54}}{{100}}(0.54,{\text{ 54 % }})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><br><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for numerator, follow through from their diagram, <strong><em>(A1)</em>(ft)</strong> for denominator. Follow through from total or denominator used in part (c).</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{10}}{{100}} \times \frac{9}{{99}} = \frac{1}{{110}}(0.00909,{\text{ 0}}{\text{.909 % }})\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><br><span><strong>Notes:</strong> Award <strong><em>(A1)</em>(ft)</strong> for their correct fractions, <em><strong>(M1)</strong></em> for multiplying</span> <span>two fractions, <strong><em>(A1)</em>(ft)</strong> for their correct answer.</span> <span>Answer 0.009 with no working receives no marks. </span><span>Follow through from denominator in parts (c) and (e) and from</span> <span>their diagram.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">A.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>H<sub>0</sub> : The (average) number of meals per day a student has and gender are independent <em><strong>(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> For “independent” accept “not associated” but do not accept “not related” or “not correlated”.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5.99 (accept 5.991) <em><strong>(A1)</strong></em><strong>(ft)</strong> </span></p>
<p><br><span><strong>Note:</strong> Follow through from their part (b).</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{28 \times 45}}{{100}} = 12.6 = 13\) or \(\frac{{28}}{{100}} \times \frac{{25}}{{100}} \times 100 = 12.6 = 13\) <em><strong>(M1)(A1)(AG)</strong></em> </span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for correct formula and <em><strong>(A1)</strong></em> for correct substitution. Unrounded answer must be seen for the <em><strong>(A1)</strong></em> to be awarded.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<p> </p>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.0321 <em><strong>(G2)</strong></em></span></p>
<p><br><span><strong>Note:</strong> For 0.032 award <em><strong>(G1)(G1)(AP)</strong></em>. For 0.03 with no working award <em><strong>(G0)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>0.0321 < 5.99 or 0.984 > 0.05 <em><strong>(R1)</strong></em></span></p>
<p><span>accept H<sub>0</sub> <strong><em>(A1)</em>(ft)</strong> </span></p>
<p><br><span><strong>Note:</strong> If reason is incorrect both marks are lost, do not award <em><strong>(R0)(A1)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">B.f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was in general well done. Candidates began the paper well by drawing the Venn diagram correctly. Some students omitted the rectangle (universal set) around the three circles. There were quite a few errors in (c) as some students forgot to convert their answers to percentages. Also describing in words what the students in \(X \cap Y'\) had for breakfast seemed to be difficult for the majority of the candidates. Some misread what <em>Y</em> was and even more missed the complement sign. However, the main problem in answering this question seemed to be the lack of knowledge in the relationship between set theory and logic (use of</span> <span style="font-size: medium; font-family: times new roman,times;">"and" and "or"). Combining probabilities caused problems to many. Common wrong answers were \(\frac{{10}}{{100}}\), \(\frac{{10}}{{100}} \times \frac{{10}}{{100}}\) or \(\frac{{10}}{{100}} + \frac{9}{{99}}\).</span></p>
<div class="question_part_label">A.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">In general this part question was well answered. The major concerns of the examining team were the following:</span></p>
<ul>
<li><span style="font-family: times new roman,times; font-size: medium;">In (f) many students wrote down the expected values table (from the GDC) and highlighted the correct expected value, 12.6. As this is a "show that" question the use of the GDC is not expected and therefore no marks are awarded for this working. Instead it is expected the use of the formula for the expected value with the correct substitutions.</span></li>
<li><span style="font-family: times new roman,times; font-size: medium;">In (e) surprisingly many candidates found the \(\chi _{calc}^2\) through the use of the formula. </span><span style="font-family: times new roman,times; font-size: medium;">Unfortunately this led to some incorrect answers and also to a bad use of time. The </span><span style="font-family: times new roman,times; font-size: medium;">question clearly says "use your graphic display calculator" and it is worth 2 marks </span><span style="font-family: times new roman,times; font-size: medium;">therefore a student should not spend more than 2 minutes to answer this part </span><span style="font-family: times new roman,times; font-size: medium;">question. Time management is essential in this type of examinations and the IB rule </span><span style="font-family: times new roman,times; font-size: medium;">is one minute – one mark.</span></li>
</ul>
<div class="question_part_label">B.f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Sharon and Lisa share a flat. Sharon cooks dinner three nights out of ten.</span> <span style="font-size: medium; font-family: times new roman,times;">If Sharon does not cook dinner, then Lisa does. If Sharon cooks dinner </span><span style="font-size: medium; font-family: times new roman,times;">the probability that they have pasta is 0.75. If Lisa cooks dinner the probability</span> <span style="font-size: medium; font-family: times new roman,times;">that they have pasta is 0.12.</span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">A survey was carried out in a year 12 class. The pupils were asked which pop groups they like out of the <em>Rockers</em> (<em>R</em>), the <em>Salseros</em> (<em>S</em>), and the <em>Bluers</em> (<em>B</em>). The results are shown in the following diagram.</span></p>
<p style="text-align: center;"><img src="data:image/png;base64,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" alt></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span><strong>Copy and complete</strong> the tree diagram to represent this information.</span></p>
<p><span><img 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" alt></span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that Lisa cooks dinner and they do not have pasta.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the probability that they do not have pasta.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Given that they do not have pasta, find the probability that Lisa cooked dinner.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down \(n(R \cap S \cap B)\).</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find \(n(R')\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Describe which groups the pupils in the set \(S \cap B\) like.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use set notation to describe the group of pupils who like the <em>Rockers</em> and the <em>Bluers</em> but do not like the <em>Salseros.</em></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There are 33 pupils in the class.</span></p>
<p><span>Find <em>x</em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii, e, i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>There are 33 pupils in the class.</span></p>
<p><span>Find the number of pupils who like the <em>Rockers.</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ii, e, ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt><br></span></p>
<p><span><br><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair. <em><strong>(A3)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.7 \times 0.88 = 0.616{\text{ }}\left( {\frac{{77}}{{125}},{\text{ }}61.6{\text{ }}\% } \right)\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying the correct probabilities.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(0.3 \times 0.25 + 0.7 \times 0.88\) <em><strong>(M1)(M1)</strong></em></span></p>
<p><br><span><strong>Notes:</strong> Award <em><strong>(M1)</strong></em> for a relevant two-factor product, could be \(S \times NP\) <strong>OR </strong>\(L \times NP\).</span></p>
<p><span>Award <em><strong>(M1)</strong></em> for summing 2 two-factor products.</span></p>
<p><span><br>\({\text{P}} = 0.691{\text{ }}\left( {\frac{{691}}{{1000}},{\text{ }}69.1{\text{ }}\% } \right)\) </span><span><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em> </span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Notes: (ft)</strong> from their answer to (b).</span></p>
<p><span> </span></p>
<p><em><strong><span>[3 marks]</span></strong></em></p>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{0.616}}{{0.691}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><br><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for substituted conditional probability formula,</span> <span><em><strong>(A1)</strong></em> for correct substitution.<br><br></span></p>
<p><span>\({\text{P}} = 0.891{\text{ }}\left( {\frac{{616}}{{691}},{\text{ }}89.1{\text{ }}\% } \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">i, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>3 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>For 5, 4, 7 (0) seen with no extra values <em><strong>(A1)</strong></em></span></p>
<p><span>16 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">ii, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>They like (both) the <em>Salseros (S)</em> <strong>and</strong> they like the<em> Bluers (B) </em> <em><strong>(A1)(A1)</strong></em></span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <strong><em>(A1)</em></strong> for “and”, <em><strong>(A1)</strong></em> for the correct groups.</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">ii, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(R \cap B \cap S'\) <em><strong>(A1)(A1)</strong></em> </span></p>
<p><strong><em> </em></strong></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for \(R \cap B\), <em><strong>(A1)</strong></em> for \( \cap S'\)</span></p>
<p><span> </span></p>
<p><em><strong><span>[2 marks]</span></strong></em></p>
<div class="question_part_label">ii, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(21+ 3x = 33\) <em><strong>(M1)</strong></em></span></p>
<p><span>\(x = 4\) <em><strong>(A1)(G2)<br></strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">ii, e, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>17 <strong><em>(A1)</em>(ft)</strong></span></p>
<p><span><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">ii, e, ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The tree diagram was quite well answered by many students, but sometimes it was missing on many papers. It seemed they had it on their examination paper because the subsequent questions were answered accurately. Conditional probability was of great difficulty to many candidates.</span></p>
<div class="question_part_label">i, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The tree diagram was quite well answered by many students, but sometimes it was missing on many papers. It seemed they had it on their examination paper because the subsequent questions were answered accurately. Conditional probability was of great difficulty to many candidates.</span></p>
<div class="question_part_label">i, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The tree diagram was quite well answered by many students, but sometimes it was missing on many papers. It seemed they had it on their examination paper because the subsequent questions were answered accurately. Conditional probability was of great difficulty to many candidates.</span></p>
<div class="question_part_label">i, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">The tree diagram was quite well answered by many students, but sometimes it was missing on many papers. It seemed they had it on their examination paper because the subsequent questions were answered accurately. Conditional probability was of great difficulty to many candidates.</span></p>
<div class="question_part_label">i, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled although part (d) proved too difficult for many candidates and</span> <span style="font-size: medium; font-family: times new roman,times;">demonstrated, overall, a poor level of understanding of basic set notation. Students generally </span><span style="font-size: medium; font-family: times new roman,times;">had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled although part (d) proved too difficult for many candidates and</span> <span style="font-size: medium; font-family: times new roman,times;">demonstrated, overall, a poor level of understanding of basic set notation. Students generally </span><span style="font-size: medium; font-family: times new roman,times;">had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled although part (d) proved too difficult for many candidates and</span> <span style="font-size: medium; font-family: times new roman,times;">demonstrated, overall, a poor level of understanding of basic set notation. Students generally </span><span style="font-size: medium; font-family: times new roman,times;">had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled although part (d) proved too difficult for many candidates and</span> <span style="font-size: medium; font-family: times new roman,times;">demonstrated, overall, a poor level of understanding of basic set notation. Students generally </span><span style="font-size: medium; font-family: times new roman,times;">had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was well handled although part (d) proved too difficult for many candidates and</span> <span style="font-size: medium; font-family: times new roman,times;">demonstrated, overall, a poor level of understanding of basic set notation. Students generally </span><span style="font-size: medium; font-family: times new roman,times;">had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, e, i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well handled although part (d) proved too difficult for many candidates and demonstrated, overall, a poor level of understanding of basic set notation. Students generally had the algebraic skills required to solve for <em>x</em> in part (e)(ii).</span></p>
<div class="question_part_label">ii, e, ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">The seniors from Gulf High School are required to participate in exactly one after-school sport. Data were gathered from a sample of 120 students regarding their choice of sport. The following data were recorded.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">A \({\chi ^2}\) test was carried out at the 5 % significance level to analyse the relationship between gender and choice of after-school sport.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the null hypothesis, H<sub>0</sub>, for this test.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find the expected value of female footballers.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the critical value of \(\chi ^2\), at the 5 % level of significance.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Use your graphic display calculator to determine the \(\chi _{calc}^2\) value.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Determine whether H<sub>0</sub> should be accepted. Justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One student is chosen at random from the 120 students.</span></p>
<p><span>Find the probability that this student</span></p>
<p><span>(i) is male;</span></p>
<p><span>(ii) plays tennis.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two students are chosen at random from the 120 students.</span></p>
<p><span>Find the probability that</span></p>
<p><span>(i) both play football;</span></p>
<p><span>(ii) neither play basketball.</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>H<sub>0</sub> : Gender and choice of afterschool sport are independent. <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> Accept “not associated”, do not accept “not related”, “not correlated”, or “not linked”. Accept “the relation between gender and sport is independent”.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{85}}{{120}} \times \frac{{48}}{{120}} \times 120\left( {\frac{{85 \times 48}}{{120}}} \right)\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct expression.</span></p>
<p> </p>
<p><span>= 34 <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2 <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>5.99 (5.991) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> Follow through from part (c).</span></p>
<p><span><em><strong>[1 mark]</strong></em></span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>2.42 (2.42094…) <em><strong>(G2)</strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>Since 2.42 < 5.99 therefore accept (do not reject) H<sub>0</sub> <em><strong>(R1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Note:</strong> The numerical values need not be seen, but must be consistent with their parts (d) and (e).</span></p>
<p><span><br><strong>OR</strong></span></p>
<p><span><em>p-value</em> 0.298 > 0.05 therefore accept (do not reject) H<sub>0</sub> <em><strong>(R1)(A1)</strong></em></span></p>
<p><span><strong>Note:</strong> <em>p-value</em> comparison may <strong>not</strong> be used as part of a follow through solution. Do not award <em><strong>(A1)(R0)</strong></em>. Follow through from parts (c), (d) and (e).<br></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{35}}{{120}}\left( {\frac{7}{{24}},{\text{ }}0.292,{\text{ }}29.2\% } \right)\) (0.291666...) <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span>(ii) \(\frac{{25}}{{120}}\left( {\frac{5}{{24}},{\text{ }}0.208,{\text{ }}20.8\% } \right)\) (0.208333...) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[2 marks]</strong></em></span></p>
<p> </p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{48}}{{120}} \times \frac{{47}}{{119}}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct fractions, <em><strong>(M1)</strong></em> for multiplying their two fractions.</span></p>
<p><br><span>\( = \frac{{94}}{{595}}(0.158,{\text{ }}15.8\% )\) (0.157983...) <em><strong>(A1)(G2)</strong></em></span></p>
<p> </p>
<p><span>(ii) \(\frac{{73}}{{120}} \times \frac{{72}}{{119}}\) <em><strong>(M1)</strong></em></span></p>
<p><span><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for multiplying correct fractions. If sampling with replacement has been used in both parts (h)(i) and (h)(ii) do not penalise in part (h)(ii). Award a maximum of <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong>.</span></p>
<p> </p>
<p><span>\( = \frac{{219}}{{595}}(0.368,{\text{ }}36.8\% )\) (0.368067...) <em><strong>(A1)(G2)</strong></em></span></p>
<p><span><em><strong> </strong></em></span></p>
<p><span><em><strong>[5 marks]</strong></em></span></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">This question was successfully attempted by the great majority. However, the test is for the mathematical independence of the two variables; it does not address “correlation” or whether there is “no relation” between them. Further, the result of the test should be determined by the comparison of the <strong>numerical values</strong> of either the chi-squared calculated and critical values or the associated <em>p</em>-value and the significance level of the test. The creeping use of <em>k</em> as the critical value is the notation used in one text book; it is <strong>not</strong> standard notation and its use is not accepted. Comments were made on the G2 forms as to whether the the null hypothesis should be “accepted” or not rejected; both forms are acceptable.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">In the compound probability questions, the lack of an explicit tree diagram determined that many candidates were not able to proceed. Determining an appropriate technique is a skill that should be taught.</span></p>
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A group of <span class="s1">100 </span>customers in a restaurant are asked which fruits they like from a choice of mangoes, bananas and kiwi fruits. The results are as follows.</p>
<p class="p1"><span class="s1"> 15 </span>like all three fruits</p>
<p class="p1"><span class="s1"> 22 </span>like mangoes and bananas</p>
<p class="p1"><span class="s1"> 33 </span>like mangoes and kiwi fruits</p>
<p class="p1"><span class="s1"> 27 </span>like bananas and kiwi fruits</p>
<p class="p1"><span class="s1"> 8 </span>like none of these three fruits</p>
<p class="p1"> \(x\) like <strong>only </strong>mangoes</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><strong>Copy </strong>the following Venn diagram and correctly insert all values from the above information.</p>
<p class="p1"><img src="images/Schermafbeelding_2015-12-22_om_06.31.28.png" alt></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Complete your Venn diagram from part (a) with this additional information <strong>in terms </strong><strong>of</strong> \(x\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Find the value of \(x\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Write down the number of customers who like</p>
<p class="p1">(i) mangoes;</p>
<p class="p1">(ii) mangoes or bananas.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">A customer is chosen at random from the <span class="s1">100 </span>customers. Find the probability that this customer</p>
<p class="p1">(i) likes none of the three fruits;</p>
<p class="p1">(ii) likes only two of the fruits;</p>
<p class="p1">(iii) likes all three fruits given that the customer likes mangoes and bananas.</p>
<div class="marks">[4]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">The number of customers that like <strong>only </strong>mangoes is equal to the number of customers that like <strong>only </strong>kiwi fruits. This number is half of the number of customers that like <strong>only </strong>bananas.</p>
<p class="p1">Two customers are chosen at random from the <span class="s1">100 </span>customers. Find the probability that the two customers like none of the three fruits.</p>
<div class="marks">[3]</div>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="data:image/png;base64,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" alt> <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)(A1)</em></strong></p>
<p class="p1"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for <span class="s1">15 </span>in the correct place.</p>
<p class="p1">Award <strong><em>(A1) </em></strong>for <span class="s1">7, 18 </span>and <span class="s1">12 </span>seen in the correct places.</p>
<p class="p1">Award <strong><em>(A1) </em></strong>for <span class="s1">8 </span>in the correct place.</p>
<p class="p1">Award at most <strong><em>(A0)(A1)(A1) </em></strong>if diagram is missing the rectangle.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img 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" alt> <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for \(x\) seen in the correct places.</p>
<p class="p1">Award <strong><em>(A1) </em></strong>for \(2x\) seen in the correct place.</p>
<p class="p1">Award <strong><em>(A0)(A1)</em>(ft) </strong>if \(x\) and \(2x\) are replaced by <span class="s1">10 </span>and <span class="s1">20 </span>respectively.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(2x + x + x + 15 + 8 + 7 + 18 + 12 = 100\;\;\;(4x + 60 = 100{\text{ or equivalent)}}\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(M1) </em></strong>for equating the sum of the elements of their Venn diagram to \(100\). Equating to \(100\)<span class="s1"> </span>may be implied.</p>
<p class="p2"> </p>
<p class="p1">\((x = ){\text{ }}10\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their Venn diagram. The answer must be a positive integer.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \(50\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> \(82\)</span> <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their answer to part (c) and their Venn diagram.</p>
<p class="p1">Award <strong><em>(A0)</em>(ft)<em>(A1)</em>(ft) </strong>if answer is \(\frac{{50}}{{100}}\) and \(\frac{{82}}{{100}}\).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(\frac{8}{{100}}\;\;\;\left( {\frac{2}{{25}};{\text{ }}0.08;{\text{ }}8\% } \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Correct answer only. There is no follow through.</p>
<p class="p1"> </p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(\frac{{37}}{{100}}\;\;\;(0.37,{\text{ }}37\% )\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)</strong></p>
<p class="p1"><strong>Note: </strong>Follow through from their Venn diagram.</p>
<p class="p2"> </p>
<p class="p1">(iii) <span class="Apple-converted-space"> </span>\(\frac{{15}}{{22}}\;\;\;(0.681;{\text{ }}0.682;{\text{ }}68.2\% )\;\;\;(0.681818 \ldots )\) <span class="Apple-converted-space"> </span><strong><em>(A1)(A1)</em>(ft)<em>(G2)</em></strong></p>
<p class="p1"><strong>Notes: </strong>Award <strong><em>(A1) </em></strong>for numerator, <strong><em>(A1)</em>(ft) </strong>for denominator, follow through from their Venn diagram. Award <strong><em>(A0)(A0) </em></strong>if answer is given as incorrect reduced fraction without working.</p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\frac{8}{{100}} \times \frac{7}{{99}}\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(M1)</em></strong></p>
<p class="p1"><strong>Note: </strong>Award <strong><em>(A1)</em>(ft) </strong>for correct fractions, follow through from their answer to part (e)(i), <strong><em>(M1) </em></strong>for multiplying their fractions.</p>
<p class="p2"> </p>
<p class="p1">\( = \frac{{56}}{{9900}}\;\;\;\left( {\frac{{14}}{{2477}},{\text{ }}0.00565656 \ldots ,{\text{ }}0.00566,{\text{ }}0.0056,{\text{ }}0.566\% } \right)\) <span class="Apple-converted-space"> </span><strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<div class="question_part_label">f.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Neil has three dogs. Two are brown and one is grey. When he feeds the dogs, Neil uses three bowls and gives them out randomly. There are two red bowls and one yellow bowl. This information is shown on the tree diagram below.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">There are 49 mice in a pet shop.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">30 mice are white.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">27 mice are male.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">18 mice have short tails.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">8 mice are white and have short tails.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">11 mice are male and have short tails.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">7 mice are male but neither white nor short-tailed.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">5 mice have all three characteristics and</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">2 have none.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;">Copy the diagram below to your examination script.</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"><img 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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One of the dogs is chosen at random.</span></p>
<p><span>(i) Find P (the dog is grey and has the yellow bowl).</span></p>
<p><span>(ii) Find P (the dog does not get the yellow bowl).</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Neil often takes the dogs to the park after they have eaten. He has noticed that the grey dog plays with a stick for a quarter of the time and both brown dogs play with sticks for half of the time. This information is shown on the tree diagram below.</span></p>
<p><span><img src="data:image/png;base64,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" alt></span></p>
<p><span>(i) Copy the tree diagram and add the four missing probability values on the branches that refer to playing with a stick.</span></p>
<p><span>During a trip to the park, one of the dogs is chosen at random.</span></p>
<p><span>(ii) Find P (the dog is grey or is playing with a stick, but not both).</span></p>
<p><span>(iii) Find P (the dog is grey given that the dog is playing with a stick).</span></p>
<p><span>(iv) Find P (the dog is grey and was fed from the yellow bowl and is not playing with a stick).</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Complete the diagram, using the information given in the question.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Find (i) \(n(M \cap W)\)</span></p>
<p><span>(ii) \(n(M′ \cup S)\)</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two mice are chosen without replacement.</span></p>
<p><span>Find P (both mice are short-tailed).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) P (a dog is grey and has the yellow bowl)</span></p>
<p><span>\( = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}( = 0.111)\) <em><strong>(M1)(A1)(G2)</strong></em></span></p>
<p><em><span>The <strong>(M1)</strong> is for multiplying two values along any</span> <span>branch of the tree.</span></em></p>
<p><br><span>(ii) P (dog does not get yellow bowl) \( = \frac{2}{3}\) </span><span>( = 0.667 (3sf)</span> <span>or </span><span>0.6) <em><strong>(A1)</strong></em></span></p>
<p> </p>
<p><span><em><strong>[3 marks]</strong></em></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) The tree diagram should show the values</span><span> \(\frac{1}{2},\frac{1}{2}\)</span> <span>for the</span> <span>brown branch and \(\frac{1}{4},\frac{3}{4}\)</span> <span>in the correct positions for </span><span>the grey branch. <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></span></p>
<p><em><span>Follow through if the branches are interchanged.</span></em></p>
<p><br><span>(ii) P (the dog is grey or is playing with a stick, but not</span> <span>both)</span></p>
<p><span>\( = \frac{1}{3} \times \frac{3}{4} + \frac{2}{3} \times \frac{1}{2}\) <em><strong>(M1)</strong></em></span></p>
<p><span>\( = \frac{7}{{12}}\) ( = 0.583) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><em><span>The <strong>(M1)</strong> is for showing two correct products</span> <span>(whether added or not).</span> <span>Follow through from b(i).</span></em> <span><em>Award <strong>(M1)</strong> for</em> \(</span><span> \frac{1}{3} + \frac{1}{4}\)</span> <em><span>(must be a sum).</span></em></p>
<p><br><span>(iii) P (dog is grey given that it is playing with stick)</span></p>
<p><span>\(\frac{{P(G \cap S)}}{{P(S)}} = \frac{{\frac{1}{3} \times \frac{1}{4}}}{{\left( {\frac{2}{3} \times \frac{1}{2}} \right) + \left( {\frac{1}{3} \times \frac{1}{4}} \right)}}\) or \(\frac{1}{{12}}/\frac{5}{{12}}\) <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><em><span><strong>(M1)</strong> for substituted conditional probability formula,</span> <span><strong>(A1)</strong> for correct substitutions.</span></em></p>
<p><span>\( = \frac{1}{5}\) ( = 0.2) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></span> </p>
<p> </p>
<p><span>(iv) P (grey and fed from yellow bowl and not playing </span><span>with stick) \( = \frac{1}{3} \times \frac{1}{3} \times \frac{3}{4} = \frac{1}{{12}}\) ( = \(\frac{3}{{36}}\) </span><span>= 0.0833 3sf). <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><em><span><strong>(M1)</strong> is for product of 3 reasonable probability values.</span></em></p>
<p><em><span> </span></em></p>
<p><em><span><strong>[9 marks]</strong><br></span></em></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img 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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></span></span></p>
<p><em><span>Award <strong>(A1)</strong> for 2 (must be in a box), <strong>(A1)</strong> for 7, </span></em><strong><span><em> (A1)</em>(ft) </span></strong><span>for</span><em><span> 6 and 4, </span></em><strong><span><em>(A1)</em>(ft)</span></strong><em><span> for 9 and 13. Observe the assignment of </span></em><span><strong>(ft)</strong></span><em><span> marks strictly here. Example A common error is likely to be 11 instead of 6 <strong>(A0).</strong> In this case follow through to 4 and 18 </span></em><strong><span><em>(A1)</em>(ft) </span></strong><em><span>for the final pair. Here the 4 follows from the total of 27 for n(M).</span></em></p>
<p><em><span><strong>[4 marks]</strong><br></span></em></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(n(M \cap W) = 14\) <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong> </strong></span></p>
<p><span>(ii) \(n(M' \cup S) = 22 + 11\) <strong>OR</strong> \(15 + 18\) <em><strong>(A1)</strong></em><strong>(ft)</strong><br></span></p>
<p><span>= 33</span><span> <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><em>Award <strong>(A2)</strong> if answer 33 is seen. Award <strong>(A1)</strong> for any of 22, 11, 15 or 18 seen but 33 absent.</em><strong><br></strong></span></p>
<p><span><em> </em></span></p>
<p><span><em><strong>[3 marks]</strong><br></em></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>P (both mice short-tailed) \( = \frac{{18}}{{49}} \times \frac{{17}}{{48}} = \frac{{306}}{{352}}\) (= 0.130). <em><strong>(M1)(A1)</strong></em><strong>(ft)</strong><em><strong>(G1)</strong></em></span></p>
<p><span><em>(Allow alternatives such as 153/1176 or 51/392.) Award <strong>(M1)</strong> for any of</em> \(\frac{{18}}{{49}}\)</span><span> <em>and</em> \(\frac{{17}}{{48}}\)</span><span> <em>or </em>\(\frac{{18}}{{49}} \times \frac{{17}}{{49}}\)</span><span><span> <em>or</em> \(\frac{{18}}{{49}} + \frac{{17}}{{48}}\)</span></span><span> <em>seen.</em><br></span></p>
<p><span><em><strong>[2 marks]</strong><br></em></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(i) (a),(b) Elementary probability calculations were performed well and compound ones often poorly. Filling in of the tree diagram in b(i) was quite well done. Conditional probability in particular was poorly implemented.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(i) (a),(b) Elementary probability calculations were performed well and compound ones often poorly. Filling in of the tree diagram in b(i) was quite well done. Conditional probability in particular was poorly implemented.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">(ii) Most candidates had some idea how to fill in the numbers on the diagram. Full marks were common here and most candidates got some of the marks.<br></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;"> Part b(i) was handled better than b(ii), with the complement causing problems. Extensive follow-through was used here from (a).</span></p>
<p><span style="font-size: medium; font-family: times new roman,times;"> </span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-size: medium; font-family: times new roman,times;">Part (c) was rarely completed, perhaps due to time constraints, but also due to lack of understanding.</span></p>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="specification">
<p>On one day 180 flights arrived at a particular airport. The distance travelled and the arrival status for each incoming flight was recorded. The flight was then classified as on time, slightly delayed, or heavily delayed.</p>
<p>The results are shown in the following table.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A <em>χ</em><sup>2</sup> test is carried out at the 10 % significance level to determine whether the arrival status of incoming flights is independent of the distance travelled.</p>
</div>
<div class="specification">
<p>The critical value for this test is 7.779.</p>
</div>
<div class="specification">
<p>A flight is chosen at random from the 180 recorded flights.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the alternative hypothesis.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the expected frequency of flights travelling at most 500 km and arriving slightly delayed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the number of degrees of freedom.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the <em>χ</em><sup>2</sup> statistic.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the associated <em>p</em>-value.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State, with a reason, whether you would reject the null hypothesis.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that this flight arrived on time.</p>
<div class="marks">[2]</div>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that this flight was not heavily delayed, find the probability that it travelled between 500 km and 5000 km.</p>
<div class="marks">[2]</div>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Two flights are chosen at random from those which were slightly delayed.</p>
<p>Find the probability that each of these flights travelled at least 5000 km.</p>
<div class="marks">[3]</div>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>The arrival status is dependent on the distance travelled by the incoming flight <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Accept “associated” or “not independent”.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{60 \times 45}}{{180}}\) <strong>OR </strong>\(\frac{{60}}{{180}} \times \frac{{45}}{{180}} \times 180\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for correct substitution into expected value formula.</p>
<p>= 15 <em><strong> (A1) (G2)</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>4 <em><strong>(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A0)</strong></em> if “2 + 2 = 4” is seen.</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9.55 (9.54671…) <em><strong>(G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(G1)</strong></em> for an answer of 9.54.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.0488 (0.0487961…) <em><strong>(G1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Reject the Null Hypothesis <em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their hypothesis in part (a).</p>
<p>9.55 (9.54671…) > 7.779 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>OR </strong></p>
<p>0.0488 (0.0487961…) < 0.1 <em><strong>(R1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Do not award <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(R0)</strong></em><strong>(ft)</strong>. Follow through from part (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for a correct comparison, <em><strong>(A1)</strong></em><strong>(ft)</strong> for a consistent conclusion with the answers to parts (a) and (d). Award <em><strong>(R1)</strong></em><strong>(ft)</strong> for <em>χ</em><sup>2</sup><em><sub>calc</sub></em> > <em>χ</em><sup>2</sup><em><sub>crit </sub></em>, provided the calculated value is explicitly seen in part (d)(i).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{52}}{{180}}\,\,\left( {0.289,\,\,\frac{{13}}{{45}},\,\,28.9\,{\text{% }}} \right)\) <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{35}}{{97}}\,\,\left( {0.361,\,\,36.1\,{\text{% }}} \right)\) <em><strong>(A1)(A1) (G2)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{14}}{{45}} \times \frac{{13}}{{44}}\) <em><strong>(A1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for two correct fractions and <em><strong>(M1)</strong></em> for multiplying their two fractions.</p>
<p>\( = \frac{{182}}{{1980}}\,\,\left( {0.0919,\,\,\frac{{91}}{{990}},\,0.091919 \ldots ,\,9.19\,{\text{% }}} \right)\) <em><strong>(A1) (G2)</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">h.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">f.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">g.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">h.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">A survey of \(400\) people is carried out by a market research organization in two different cities, Buenos Aires and Montevideo. The people are asked which brand of cereal they prefer out of Chocos, Zucos or Fruti. The table below summarizes their responses.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">The following table shows the cost in \({\text{AUD}}\) of seven paperback books chosen at random, together with the number of pages in each book.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><img src="data:image/png;base64,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" alt></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>One person is chosen at random from those surveyed. Find the probability that this person</span></p>
<p><span>(i) does not prefer Zucos;</span></p>
<p><span>(ii) prefers Chocos, given that they live in Montevideo.</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Two people are chosen at random from those surveyed. Find the probability that they both prefer Fruti.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State the null hypothesis.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State the number of degrees of freedom.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>Show that the expected frequency for the number of people who live in Montevideo and prefer Zucos is \(63\).</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>Write down the chi-squared statistic for this data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.f.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>The market research organization tests the survey data to determine whether the brand of cereal preferred is associated with a city. A chi-squared test at the \(5\% \) level of significance is performed.</span></p>
<p><span>State whether the market research organization would accept the null hypothesis. Clearly justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">i.g.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Plot these pairs of values on a scatter diagram. Use a scale of \(1{\text{ cm}}\) to represent \(50\) pages on the horizontal axis and </span><span><span>\(1{\text{ cm}}\)</span> to represent \(1{\text{ AUD}}\) on the vertical axis.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Write down the linear correlation coefficient, \(r\), for the data.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span>Stephen wishes to buy a paperback book which has \(350\) pages in it. He plans to draw a line of best fit to determine the price. State whether or not this is an appropriate method in this case and justify your answer.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span>(i) \(\frac{{280}}{{400}}{\text{ }}(0.7{\text{, }}70\% {\text{ or equivalent}})\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><strong>Note: <em>(A1)</em></strong> for correct numerator, <em><strong>(A1)</strong></em> for correct denominator.</span></p>
<p><span>(ii) \(\frac{{57}}{{210}}{\text{ }}\left( {\frac{{19}}{{70}}{\text{, }}0.271{\text{, }}27.1\% } \right)\) <em><strong>(A1)(A1)(G2)</strong></em></span></p>
<p><span><span><strong>Note: <em>(A1)</em></strong> for correct numerator,</span> <span><em><strong>(A1)</strong></em> for correct denominator.</span></span></p>
<p><span><span><em><strong>[4 marks]</strong></em><br></span></span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{180}}{{400}} \times \frac{{179}}{{399}}\) <em><strong>(A1)(M1)</strong></em></span></p>
<p><span><strong><br>Note: <em>(A1)</em></strong> for correct values seen, <em><strong>(M1)</strong></em> for multiplying their two values, <em><strong>(A1)</strong></em> for correct answer.</span></p>
<p><br><span>\( = \frac{{537}}{{2660}}{\text{ }}( = 0.202)\) <em><strong>(A1)(G3)</strong></em></span></p>
<p><span><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\({{\text{H}}_0}\) : ‘the preference of brand of cereal is independent of the city’. <em><strong>(A1)</strong></em></span></p>
<p><span><strong>OR</strong></span></p>
<p><span>\({{\text{H}}_0}\) : ‘there is no association between the brand of cereal and city’.</span></p>
<p><span><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(df = 2\) <em><strong>(A1)</strong></em></span></p>
<p><span><em><strong>[1 mark]<br></strong></em></span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(\frac{{210 \times 120}}{{400}}\) <em><strong>(M1)(A1)</strong></em></span></p>
<p><span><strong>Note: <em>(M1)</em></strong> for substituting in correct formula, <em><strong>(A1)</strong></em> for correct values.</span></p>
<p><span>\( = 63\) <em><strong>(AG)</strong></em></span></p>
<p><span><span><strong>Note: </strong>Final line must be seen or previous</span> <span><em><strong>(A1)</strong></em> mark is lost.</span></span></p>
<p><span><span><em><strong>[2 marks]</strong></em><br></span></span></p>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(39.3\) <em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note: </strong>Award <em><strong>(G1)(A0)(AP)</strong></em> if answers not to 3 significant figures.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">i.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(p - {\text{value}} < 0.05\) <em><strong>(R1)</strong></em><strong>(ft)</strong></span></p>
<p><span>Do not accept \({{{\text{H}}_0}}\) . <em><strong>(A1)</strong></em><strong>(ft)</strong></span></p>
<p><span><strong>Notes: </strong>Allow ‘Reject \({{{\text{H}}_0}}\) or equivalent’. <strong>(ft)</strong> from their \({\chi ^2}\) statistic.</span><br><span>Award <strong><em>(R1)</em>(ft)</strong> for comparing the appropriate values. <strong><em>(A1)</em>(ft)</strong> can be awarded only if the conclusion is valid according to the comparison given. If no reason given or if reason is wrong both marks are lost. Note that <strong><em>(R1)(A0)</em>(ft)</strong> can be awarded but <strong><em>(R0)(A1)</em>(ft)</strong> cannot.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">i.g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span><img src="data:image/png;base64,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" alt><span> <em><strong>(A1)(A1)(A1)</strong></em></span></span></p>
<p><span><strong>Notes: <em>(A1)</em></strong> for label and scales, <em><strong>(A2)</strong></em> for all points correct, <em><strong>(A1)</strong></em> for 5 or 6 correct. Award a maximum of <em><strong>(A2)</strong></em> if points are joined.</span></p>
<p><span><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>\(r = - 0.141\) <em><strong>(G2)</strong></em></span></p>
<p><span><strong>Note: </strong>If negative sign is missing award <em><strong>(G1)(G0)</strong></em>.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span>‘The coefficient of correlation is too low, (very) weak (linear) relationship’. <em><strong>(R1)</strong></em></span></p>
<p><span>Not a sensible thing to do, <em>accept ‘no’.</em> <em><strong>(A1)</strong></em></span></p>
<p><span><strong>Note: </strong>Do not award <em><strong>(R0)(A1)</strong></em>. The correlation coefficient has to be mentioned in their reasoning.</span></p>
<p><span><em><strong>[2 marks]</strong></em><br></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.e.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.f.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Candidates answered part (a) correctly. Some lost one out of the 4 marks for making an error in the denominator of the conditional probability. In (b) many students failed to see that (b) was 'without replacement'. Parts (c), (d) and (e) seemed to be very well done by some centres and uniformly badly by others. In (e) many gave the table from the GDC and highlighted the value 63 for which no mark was gained. Expected value formula should have been used instead.</span></p>
<div class="question_part_label">i.g.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph was well done with almost all candidates labelling and scaling the axes correctly. A minority of students joined the points or drew the graph on lined paper which prevented them from gaining full marks in this part of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">In (b) some candidates were not able to calculate the linear correlation coefficient. A few G2 comments pointed out that the command term used may have been ambiguous to some candidates and they did not think that they could use their GDC to find <em>r</em>. Some attempted to use the formula even though the value of \({S_{xy}}\) was not given. The guide says that 'A GDC can be used to calculate <em>r</em> when raw data is given'. This potential unfairness was taken into consideration during the setting of boundaries so that no candidate was disadvantaged by the possible ambiguous wording of the question. In future the command term 'Using your GDC' or 'Write down' will be used in similar questions.</span></p>
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Some students who did use the GDC gave \({r^2}\) instead of</span> <span style="font-family: times new roman,times;">\(r\)</span><span style="font-family: times new roman,times;">.</span> <span style="font-family: times new roman,times;">This really caught the attention of many examiners as \({r^2}\) is not in the syllabus.</span></span></p>
<div class="question_part_label">ii.a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph was well done with almost all candidates labelling and scaling the axes correctly. A minority of students joined the points or drew the graph on lined paper which prevented them from gaining full marks in this part of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">In (b) some candidates were not able to calculate the linear correlation coefficient. A few G2 comments pointed out that the command term used may have been ambiguous to some candidates and they did not think that they could use their GDC to find <em>r</em>. Some attempted to use the formula even though the value of \({S_{xy}}\) was not given. The guide says that 'A GDC can be used to calculate <em>r</em> when raw data is given'. This potential unfairness was taken into consideration during the setting of boundaries so that no candidate was disadvantaged by the possible ambiguous wording of the question. In future the command term 'Using your GDC' or 'Write down' will be used in similar questions.</span></p>
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Some students who did use the GDC gave \({r^2}\) instead of</span> </span><span style="font-size: medium;"><span style="font-family: times new roman,times;"><span style="font-family: times new roman,times; font-size: medium;">\(r\)</span>.</span> <span style="font-family: times new roman,times;">This really caught the attention of many examiners as \({r^2}\) is not in the syllabus.</span></span></p>
<div class="question_part_label">ii.b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">The graph was well done with almost all candidates labelling and scaling the axes correctly. A minority of students joined the points or drew the graph on lined paper which prevented them from gaining full marks in this part of the question.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">In (b) some candidates were not able to calculate the linear correlation coefficient. A few G2 comments pointed out that the command term used may have been ambiguous to some candidates and they did not think that they could use their GDC to find <em>r</em>. Some attempted to use the formula even though the value of \({S_{xy}}\) was not given. The guide says that 'A GDC can be used to calculate <em>r</em> when raw data is given'. This potential unfairness was taken into consideration during the setting of boundaries so that no candidate was disadvantaged by the possible ambiguous wording of the question. In future the command term 'Using your GDC' or 'Write down' will be used in similar questions.</span></p>
<p><span style="font-size: medium;"><span style="font-family: times new roman,times;">Some students who did use the GDC gave \({r^2}\) instead of</span> </span><span style="font-size: medium;"><span style="font-family: times new roman,times;"><span style="font-family: times new roman,times; font-size: medium;">\(r\)</span>.</span> <span style="font-family: times new roman,times;">This really caught the attention of many examiners as \({r^2}\) is not in the syllabus.</span></span></p>
<div class="question_part_label">ii.c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>\(180\) people were interviewed and asked what types of transport they had used in the last year from a choice of airplane \((A)\), train \((T)\) or bus \((B)\). The following information was obtained.</p>
<p>\(47\) had travelled by airplane</p>
<p>\(68\) had travelled by train</p>
<p>\(122\) had travelled by bus</p>
<p>\(25\) had travelled by airplane and train</p>
<p>\(32\) had travelled by airplane and bus</p>
<p>\(35\) had travelled by train and bus</p>
<p>\(20\) had travelled by all three types of transport</p>
<p>Draw a Venn diagram to show the above information.</p>
<div class="marks">[4]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the number of people who, in the last year, had travelled by</p>
<p>(i) bus only;</p>
<p>(ii) both airplane and bus but not by train;</p>
<p>(iii) at least two types of transport;</p>
<p>(iv) none of the three types of transport.</p>
<p> </p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A person is selected at random from those who were interviewed.</p>
<p>Find the probability that the person had used only one type of transport in the last year.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Given that the person had used only one type of transport in the last year, find the probability that the person had travelled by airplane.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p><em><strong>(A1)(A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for a rectangle with \(3\) intersecting clearly labelled circles.<br>Award <em><strong>(A1)</strong></em> for \(20\) in correct region.<br>Award <em><strong>(A1)</strong></em> for \(15\), \(12\), \(5\) in correct regions.<br>Award <em><strong>(A1)</strong></em> for \(75\), \(28\), \(10\) in correct regions.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(i) \(75\) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their Venn diagram.</p>
<p> </p>
<p>(ii) \(12\) <strong><em>(A1)</em>(ft)</strong></p>
<p><strong>Note:</strong> Follow through from their Venn diagram.</p>
<p> </p>
<p>(iii) \(15 + 20 + 12 + 5\) <strong><em>(M1)</em></strong></p>
<p>\( = 52\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for addition of their \(15\), \(20\), \(12\) and \(5\). Follow through from their Venn diagram.</p>
<p> </p>
<p>(iv) \(180 - 165\) <strong><em>(M1)</em></strong></p>
<p><strong>Note:</strong> Award BI for their \(165\), or a sum adding to their \(165\), seen.</p>
<p>\(15\) <strong><em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note: </strong>Follow through from their Venn diagram.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{113}}{{180}}\,\,\,(0.628,\,\,62.8\,\% ,\,\,0.62777...)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(G2)</strong></em></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for correct numerator. Follow through from their Venn diagram.<br>Award <strong><em>(A1)</em></strong> for \(180\) in the denominator.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{10}}{{113}}\,\,\,(0.0885,\,\,8.85\,\% ,\,\,0.08849...)\) <strong><em>(A1)</em>(ft)<em>(A1)</em>(ft)<em>(G2)</em></strong></p>
<p><strong>Note:</strong> Award <strong><em>(A1)</em>(ft)</strong> for correct numerator, <strong><em>(A1)</em>(ft)</strong> for correct denominator. Follow through from their Venn diagram or numerator from part (c).</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Sets and probability<br>In part (a), a surprising number of candidates could not construct the Venn diagram correctly, based on the given information. This led to problems with the rest of the parts although they were usually awarded follow-through marks in part (b). Part (b) which required interpreting the information from their Venn diagram was generally well done. Some candidates gave the probability rather than number of people. Most candidates were successful at the simple probability but many struggled with the conditional probability.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Sets and probability<br>In part (a), a surprising number of candidates could not construct the Venn diagram correctly, based on the given information. This led to problems with the rest of the parts although they were usually awarded follow-through marks in part (b). Part (b) which required interpreting the information from their Venn diagram was generally well done. Some candidates gave the probability rather than number of people. Most candidates were successful at the simple probability but many struggled with the conditional probability.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Sets and probability<br>In part (a), a surprising number of candidates could not construct the Venn diagram correctly, based on the given information. This led to problems with the rest of the parts although they were usually awarded follow-through marks in part (b). Part (b) which required interpreting the information from their Venn diagram was generally well done. Some candidates gave the probability rather than number of people. Most candidates were successful at the simple probability but many struggled with the conditional probability.</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 1: Sets and probability<br>In part (a), a surprising number of candidates could not construct the Venn diagram correctly, based on the given information. This led to problems with the rest of the parts although they were usually awarded follow-through marks in part (b). Part (b) which required interpreting the information from their Venn diagram was generally well done. Some candidates gave the probability rather than number of people. Most candidates were successful at the simple probability but many struggled with the conditional probability.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Contestants in a TV gameshow try to get through three walls by passing through doors without falling into a trap. Contestants choose doors at random.<br>If they avoid a trap they progress to the next wall.<br>If a contestant falls into a trap they exit the game before the next contestant plays.<br>Contestants are not allowed to watch each other attempt the game.</p>
<p style="text-align: center;"><img 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"></p>
<p style="text-align: left;">The first wall has four doors with a trap behind one door.</p>
<p style="text-align: left;">Ayako is a contestant.</p>
</div>
<div class="specification">
<p>Natsuko is the second contestant.</p>
</div>
<div class="specification">
<p>The second wall has five doors with a trap behind two of the doors.</p>
<p>The third wall has six doors with a trap behind three of the doors.</p>
<p>The following diagram shows the branches of a probability tree diagram for a contestant in the game.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Write down the probability that Ayako avoids the trap in this wall.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the probability that only one of Ayako and Natsuko falls into a trap while attempting to pass through a door <strong>in the first wall</strong>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><strong>Copy</strong> the probability tree diagram and write down the relevant probabilities along the branches.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap while attempting to pass through a door in the second wall.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A contestant is chosen at random. Find the probability that this contestant fell into a trap.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>120 contestants attempted this game.</p>
<p>Find the expected number of contestants who fell into a trap while attempting to pass through a door in the third wall.</p>
<div class="marks">[3]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{3}{4}\) (0.75, 75%) <em><strong>(A1)</strong></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{3}{4} \times \frac{1}{4} + \frac{1}{4} \times \frac{3}{4}\) <strong>OR </strong>\(2 \times \frac{3}{4} \times \frac{1}{4}\) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their product \(\frac{1}{4} \times \frac{3}{4}\) seen, and <em><strong>(M1)</strong></em> for adding their two products or multiplying their product by 2.</p>
<p>\( = \frac{3}{8}\,\,\,\,\left( {\frac{6}{{16}},\,\,0.375,\,\,37.5{\text{% }}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from part (a), but only if the sum of their two fractions is 1.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img 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"><em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for each correct pair of branches. Follow through from part (a).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{3}{4} \times \frac{2}{5}\) <em><strong>(M1)</strong></em></p>
<p>Note: Award <em><strong>(M1)</strong></em> for correct probabilities multiplied together.</p>
<p>\( = \frac{3}{{10}}\,\,\,\left( {0.3,\,\,30{\text{% }}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or part (a).</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(1 - \frac{3}{4} \times \frac{2}{5} \times \frac{3}{6}\) <strong>OR </strong> \(\frac{1}{4} + \frac{3}{4} \times \frac{2}{5} + \frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\) and <em><strong>(M1)</strong></em> for subtracting their correct probability from 1, or adding to their \(\frac{1}{4} + \frac{3}{4} \times \frac{2}{5}\).</p>
<p>\( = \frac{{93}}{{120}}\,\,\,\,\left( {\frac{{31}}{{40}},\,\,0.775,\,\,77.5{\text{% }}} \right)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G2)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram.</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6} \times 120\) <em><strong>(M1)(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for \(\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,\,\,\left( {\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\,\,{\text{OR}}\,\,\frac{{27}}{{120}}\,\,{\text{OR}}\,\,\frac{9}{{40}}} \right)\) and <em><strong>(M1)</strong></em> for multiplying by 120.</p>
<p>= 27 <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong> (G3)</strong></em></p>
<p><strong>Note:</strong> Follow through from their tree diagram or their \(\frac{3}{4} \times \frac{3}{5} \times \frac{3}{6}\) from their calculation in part (d)(ii).</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A group of students at Dune Canyon High School were surveyed. They were asked which of the following products: books (B), music (M) or films (F), they downloaded from the internet.</p>
<p>The following results were obtained:</p>
<p>100 students downloaded music;<br>95 students downloaded films;<br>68 students downloaded films and music;<br>52 students downloaded books and music;<br>50 students downloaded films and books;<br>40 students downloaded all three products;<br>8 students downloaded books <strong>only</strong>;<br>25 students downloaded none of the three products.</p>
<p>Use the above information to complete a Venn diagram.</p>
<div class="marks">[5]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the number of students who were surveyed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>i) On your Venn diagram, shade the set \({\left( {F \cup M} \right) \cap B'}\) . Do not shade any labels or values on the diagram.</p>
<p>ii) Find \(n\left( {\left( {F \cup M} \right) \cap B'} \right)\) .</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A student who was surveyed is chosen at random.</p>
<p>Find the probability that</p>
<p>(i) the student downloaded music;</p>
<p>(ii) the student downloaded books, given that they had not downloaded films;</p>
<p>(iii) the student downloaded at least two of the products.</p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Dune Canyon High School has 850 students.</p>
<p>Find the expected number of students at Dune Canyon High School that downloaded music.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" alt></p>
<p><em><strong>(A1)(A1)(A1)(A1)(A1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for labelled sets B, M and F inside a universal set (label U is not required).<br>Award <em><strong>(A1)</strong></em> for \({\text{40}}\) in central area.<br>Award <em><strong>(A1)</strong></em> for correct \({\text{10, 12, 28}}\) in the other intersecting regions.<br>Award <em><strong>(A1)</strong></em> for \({\text{8, 20}}\) and \({\text{17}}\) in correct regions.<br>Award <em><strong>(A1)</strong></em> for correct \({\text{25}}\).</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(8 + 12 + 20 + 10 + 40 + 28 + 17 + 25\) <em><strong>(M1)</strong></em></p>
<p>\( = 160\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note: </strong>Award <em><strong>(M1)</strong></em> for adding all values. Follow through from their Venn Diagram.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i)</p>
<p><img 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Y/RPgSWI1d9k7E4H8Uk5Kx1MmUuS/twtACq5pqXm2QccGuhIACthta9R3fZp/s+xHHlqlXy/PPPy3nnnUemfvywYdK7V0+pXr1GHF0FkYC/O5vsXavQjRRF6M2IObnPv/hcXn75ZVm4aLH069dfRowYQUcS4ARBYYWADhwShaxbkLivUymPV3q2BSPY3d/Y5/Zcs2ZNbobar18/mgQXL14st99+OzWt448/Xg4ZPEjatNnDtCv1EtXBj7H9laW9pFKwIE3ZKeDq30yUoTrx1qCi6Zn4wCRw0MQ3LjDxlb3ms/FlvHWBaUBzgrb08isvywsvvCA9uneX448fJp06dxIwEzDJwiqFjvu4yhpjBqSnHFUxmqAAzz26sqVBmniu9hN9iucJo2ObKOGsLaq476xGpiM5eBAazQ5M2zhKgGFSqWB5o/LLL3PljTffpGns0EMPlVNPOVXgNAC37OLySEAlwzeWhvDAW7R4kTzw3weobfTu3ZtzfA0aNhJ6xCVpeVpGaB9xYQVU3cIiw6gngGc5XMLT4mHxw3v8MJiAUN2xY4f8/PPP8tGHH0rtWjXkzDPPkoMPPpjjHuxNF9eitMUkZBbcVBgFtP+FVIMakiUTXyxalH6BYyJjx46VcePGSdt2bdOHF0AongKW87tG/27eBcYMRgAm4JjjDKSVq1bKgw88SIY9cOAgGTp0KB0cyEysVLFnk4aw3RkUj1XFPaUkMtNoFgtLG9xb/hYTjtrfmfqOvPXWW1Kndh05a9RZ0qVzZ2poTAKX+WhUCuhQ4AZiABfzyGaZcDZ1BLLx0uAI0awaj0EqJBKJROXjTz6VZ555hvj1799f4GSAA/WSbMJD3Vrmn5Bnnt2gHPaAFyhMy6tXr5ajjz5ahg8fTucKlh3LCmgG1IUCWM7gVf44RAs5OKdNAdNU3XDwyG3imzPnF/frlK89TXzpjiI53nV13nThpVzC3SGhi84sLu4TnikDC4uOVNHJFyxYII8/8bgs/H0hO/+VV10pVQqrMB3qyhFQln751NMhBfDfC2cjJOCSDe/DYcOGybBhw+Xrr76Uf9/5b6lTp4788Y+n0esNZMRcFTdio9IIWuoiVEuaMp2d+lATJbwZAdf+A82LIkXy6SefyCOPPi4FhYVy5JFHCtYZcWBhmDDqxd7bfL2Ys32fL2dbDggqeB6OHDmSJsD3339fTj/9dDnhhBNYV/Xr1TVFUq5i17vpQ1vpSnCH7PlChHzAM4moyus5ces5UEi1WJ4CKpHBlR885hmIOJKiQEmFKj/EIEWZKGD7pzMaVeKj00ciRYJ5mIkPTZRZs2bJpZddSm+qwsIqEolGyPhg4tK6AiA73E/KOR/r0oUzSKNaoAoJMHwI7T59+8q++/aRuXPnyl133SVVqlaRiy+6WDp27OC0Xx3BWwBlb9fUckBPq3mCvMbdHu8w33f33XdLo8aNZcTIEVK7dh11WHFpR8UJp6Sayftb0ikUEsyJFhYWco4Ngvqwww6j6/yf/vQn+cPJI2X4sGFSt149NlXTUrXsVkV11XfeEyXXCxAzA4UM4OktoNLNDA3EToanCytIXzIFrFDiV2ZY4AgouI5HuZDy/vvuk++/nymjR4+Wq66+WqpWqaIj+FhMChE+yJhNNDPTw21HT8ijZHQq/G1xuLqe6SJj9eTAmqyQIAKCYh0uDEuXvfaS/9x3r8yaOVMm3DOBguKG62+g5x+FmYmUgZTsmpZGHgVXphuWaCRCxgshZwUVBgq33Xab1K5dW0aefDIXy2K+BQtakQ4HhaI10VoB55FXvj+GEEa54bADIYWyW80KThV9+vSRzz6bJueedx41qpNOOonf4htbF+ZKSVFK3eQ7vXIDf3KOhDlmv/DyFlCuDp1yZpZJApYf8FJGpLIn1BE91vTA+AQmytF5NCaRaBE98p6b9JwMP2G4jBkzRqpUrSoFYWXK2pm1F7ODu0nlVWdez91pc/gaa25wsLwknSm/Zf4heCaGpFvXbnLnHXdyLgTaJibsTzv1NDqMIAwTBQhNiS4uiMtk+pDpIuSQChu4cKxetZpaGhbWHnbY4YLFr6w3fAvcLC4AZ/qR+1kOkzdt1Gw5KcgNNAqgUIha1aBBg6Vv3/3k7bffltdef0MuuugiegWCbqhb0AuDECvYnbpOG7MAQPEUUM7h6gXFf5bCU08B5ZjnUgDKJE4n1Yu04aWKx+6Qjh1SlQDQmR20KCLzFyyQf/3zn9KqVWuZOPEhqVGjJk154ICW6e0O5Cl3GSEQnIn3mBw88GAZcMAAeXjiRDn33HNlzNgxsu+++5IBhqVAp6coUEB7FVC4dcZnxkwHj0LEuHv11dfk4UcelWOOOUaOOuoo1gWEE+rEzZTLjfdukgB0qlGjBudOEWbp1ltvFXg4wjLQpEkTNfuhjZvFzHgQ8B8fGwfauEsaudu533zF0808bS8+I6DGjh0j48aND7z4fGwfxYEq2okYdOrcsHPnTpn40EMybdo0ue6667nA1r5zGKC7kbmviwO+mz5TYaMNmQwuJoLYgrfccovUrl2LHqqYK4IwwkQ9zFJkhojmbrUmEUarAAmXLFkif73hBmncpKkcfsSRUr16dQol/dam0fNuSvJSiw0GaOmFj2EGxP2PP/4ob7zxBuvk0EMG0+sSpm14+OFgVPVSoQcflIkCSfyC/SRpoW7Oe/Gxo1rMrTmlTKUPPiovBcA80UnRFef9+qvcfMstcvBBB8lDEycyICs6NZmnAcwv8TF+SY2tvHlXxu+tSELZ6JavUofXCHp766230C394ksukfPPP18OPPBAMkLUAWlKgYW5FF1si/VMTzz5hLz5xhv0Fmzdpo0JW6SmvGSmWxlp6leZrHCyZzhSgH49evSgmfSll16S1197TW7821+5bAAsCIMy7R1+YbGbw1GZHyeC4SXkQWZAEH+Z3pWniS89sCZ1ckF8ARoAQYdk7DyuBtFIDjt27JCXXnpR3n7nHbniiitkry57cWSPyfYCG1vPTiRbEiontnfB2VBAm60Kl12Joma8Y48dIn367ic3/vWv8vVXX8v5o0drEFS6pMOdH3UUZvT1f/zjH2SS519wEb3SONfkAkzBBmHoc+d2ZVGpLi2d3GdoUojK/oc//IFBjEeNOkfGjhkjBx10sJpabR9weUVWKqJkszDoIC7ewVlTem37j4S3gEpXuLgKYEeV/qO/e0JkxzQTwWgoa9aupdmpQYMGct+99zH6gzVJoV/isEzXXOyehEu11GzL6nIPU1FhWDfnwxYV99xzjzz33HNy0YUXynXXX89RfDgmUhSN0i36//7v/7h2BwFcMZJPFk6pohSki1MAAzZrugZ9MR+FuJF33nmn/PDDD3LWWWdJ1SrK6rhnVYK3ahxOcFUOCrjlg46WM8Ja4vH2k3FDp0zn5xax6cAJ0u5SD9YkhBBECA1zwQWjZciQIXLllVdKFYQkoqXJBNh0tCZjfgrouQs9S2vnjgnVmFExJLdzGmCMI0aOlMuvuEKuvuoqLrQtikTkgQceoPs4TIAQThhUWOFkR/7JXS64T40CoCetCsaUjWu47Y8ZO5ZR1C+44AJZv2EjI3SoOmXW9wV9odx9wWHrbtrhof5PrQJLSOUtoErrtaW8B/6Jh7tEwXVqLcPQDdtiRKLy5ptvUHO6+eZb6AKtnmdmi21qWDF+BwbLf+YZOnBa+ZdS95UPtno9KhM0pTOmIgqdWEw6d+ok//3vf+Wpp56Sk0eOlF9/+VXAGBGVwn1YZup+FlynTwHQFT87CEBdYfBw1NFHM/r+qLNGcQE27d5B+0+r/7MfuHgAyAn+AuGvfQT8xZ+jBAHlTwYBlIACAQUCCgQUCCiQCgU856B8kYEuIK7LVPDcvdIkEAuLbXV7dYz+sAARo5R7771XZv88WyZMuFs3C0R8OGMXZnI792QnoSwF3d/YZ8G5ZAqY+rD0BQm5xMY14Q4vSexztHHjRtmjzR6yZs1qgbs/9s2yB0b4wZFZClga2zNy69qtm7Rs2UquufZauWD0BXL44YehBqWgoJCTs8637n4XVFWpFQXNKdNk8hRQ6bplUuVzYZ8uvFKpVZk+sHTDORaSwgLEJlPBBG+966+7Tpo3b8HYbQjVA4GlLYUJApdav9sCo87aSlETH/8agQMG99NPP8m1114rf//736Vbt31k8pQpct9993FhL7zL3JP4DkP0G88AXrEUAL3r1a8nF154kTz22GOyYsUyOfW0UxOEE2vXDObQnwJ+VSwp9aGyGUc6mdgnrsXtJaQt5ytPAZWuaAyCxZazJtyfcySHP1r1kSIswg3Lls2bZcwlYxiBAJvVYY0OZRMX6FoAxhnC3gZnHyhghJNTL3GXcDxiBPJHHqFW26x5c8quoUOPk5atWslNN90k55xzjtSrV88HPAIQqVIAGm5BjQI548wzZPIrr8jy5ctl3PjxwrCI+IOK1C4XuPuXhcjx8ZrGXM0Q28ncHBQL4C5FWUodfGMpgMleRIeIYe+bcFjWrV0n4y4bJyefPJLRriGcEHdMN9hDqgy1EIvQ7n6mcDLhizAfjI0QIxF5d+pUefTRR+W222+nQAIjxOaOqB+EQ7rxxhtl4sSJsnTpUlLQalK7OzmzXX5oUdCMEL0DAWaxi+8//t9N3M4DA0CYzjkoN/WcbfzyNj/SS134MkE6bwGF3NL+GZTThuMHLnkEwwj3ggIEvhTOa1xxxeXsWEcddTTND2CQOGB9cvbDMeROv97yiFZZaFtgbPyHeglpdPiiop0ydepUefrppxn0tUF91ZBg9UPdhCUmBSGR3j27y603/0Mee+RhWbViOdwvHeMETUmGceYtg8oDxK1wsmdM1p5w0gjZsGmLXHPt9bJzZ4TmKa1nNaUHfaiMPICfhczSFv8bg6eAMl3SOiiX/wzOykPPacMrPwb5lYIumugcUTI4kA7RCNatX8c9ibD9NQKLopNx5GAYGzStgLaZpQCZFagejdJhBZrTOxROT8ldd98lNWvVVMmFD/lf3W1NB5AuXbrI/fffzwW9K1asYMBeK5xsLDn7bXDOLAXQf6DFgv7HHnusVKlSRa66+irZvn0H4/qhz+HIbIvKc+h2wGap5HIvp5B3eH/6dekpoNIHHUAoLwWoDMQ0uCgCXW7ctFEuu/Qy+dOf/yQHHnQgOxU6GDQmu2WEMxwvb2bB92WnQEikqKhIxwWxGDWnl158Uf7977ukbt16LlMr5gx1gh2mPphfEbkAdda2bVv529//Jo88+ogsW7rMyRvv0KmDI3sUAM1xQFBhM8Q6deqybqxwsmupsodRkJMXBTwFFLxY0vpnGoEadvE3+FciBTiFpPHfCsJh2bZtm1zzl2vk9NP/KEcecSTlEEd+NjCsiVwOQVUi3OBt+hQwi0Ch3X711VfyzDPPMkpE3bp16dqv84Cq2bIuUDesH90angwxFJIunbtwYfUzzzwj69evdwYcXp0zeJ4ZCri1VwSbPfzww2X9+g1yxx13cBCCDSODPlUCBRhRxfXe9A+0c/vzq+Y8BZQvGehAxRdQ2QSCUbCjmWCEa+6h1diD2o5Rce23+kzNA/a74s+JI2aFH+LOtwjuij2D4Eo+aNAgOfSww3RUbjfZs4I/EUTx2QRPy0cBtFfzQ13bOmbg12hM5syZI3dPmCC3334bI0SwMyIHpy5Mg9eExqPCOq8gPFJIunXrJjfccL08+OCDsmXLFkd78ts0Ur6C715fc8Agwgj/VliNHHmyzJn7izz6+BPczZj1b0xZpVEHMNBv0XbQl1mXhjfwuQVg25cxIaKFsZXZdKYpkR/YNHlxVoydbuAjzt4CyhIz1bMbyVRhVFA6NmBDbTQ2xLzDj9dmoSy5EuYbEHYIcxMRvNc5JKYvCXcr0fAND3UXxyXg3H7bbdKxYyd66yGkERmhe3RSEuzgnSNkrLAp89nUBnlNyGzRXhSht96y5cu40PPmm2+WRo0bc5En1qA5Ixl7WcwZ9WfnPTDu7NWrlynFLEEAACAASURBVIwfP14eeughth22F0AKzH2mBrJ3sjTH+Y9//KN88MEH3BZl584ip26KFRiuesbAA/yAfKBI01m+QZFlTbhm4KJCDC0nJCHDX5SHFLGtsfQu+GVuvxWVhiVxeoKvlectoJxRoCPWyZPNsLL06/iwsvRv080rE+kdMgO4Hmhn2ABNBZEr7hQ96dA61KMOjbNEOvFDhal/43lMnjxZtm7dJqNGjeKrgsIC94clw80EHXZDmFqTGHzoqHjL1i1y3bXXytVXXS2tWrbU7siPrHZUSh/Ba7P4E8wJzHDgwIGMcv7EE0+wfpmXqWn3dWLlB3eZogBojkHEqaeeygXWs2f/TIHj7MprM3YaR7zO2UzsWipGGVFLC+BhYOscJi0EE0a20WhEItiWBcwizgK03eVTv9MSuIvgFDndC28BVSKHLZ16LnobHEtPkyvcVxmECiC0KYSsefDBB2T4sOPJoPr06SsnnniinHTSiXLEEYfLmWeeIZOemyRbt2yVSARrKkouK96j4XMtDbzwzPXXX38tzz77rFw27jKpUrWKq6FqI2Y6x+xQch65Qst8wcNQmDRX8w6YTEx2bN8h3DJj+HBu44BxIr9Fndl6LK2v4DvWmzI1NA9oyqeccgq353jrrbfYR+zkPARYcGSPApbeqKOaNWvKGWecIddfd71Aa7Z1jbphu0B/Te7fbAdR2b5ju2DAAW/bVi1byZlnnsk5ykhUrS/s5zGFgxcIjXXkkUdImz3ayOVXXC4fffgR81B88qN/gz48QBPbzkkff+qvhEgSaXQS4mwQB54AlUedzpY8xBA3ItWqVZVzzjlPunTpKn/605/k7LPPldGjz2fB4Mzw2KOPypVXXC0zpn8r/+///T8JFYRL1HcBnw3fmAfR+NeuWyt33nGnTLh7ArcKwOhLG6p+zWuLmD91H0CxFKCihPaq84BssqR/TJ57bpI0a9aM2g76oppz4mcLorSz3XpcwgWU2QUhhK+KyLhLL+W2EL/99pu0a9fOMQWWBi947y8F0L+0v4k0adpMjjrmWLnxb/8n/7lnArePpyUDjBftglkb7ZnWE7SckFSvVk3+/OczpEOHTnLaaX+UTz6ZJnPm/Cp77703Z5uQjsOeKLRokWnTPpPZs+dIk6ZN5fbbbne2cGEDyWV+mcTawctAFf58xrsEDSq9BlDZeCnmG2rVqkkNCWsn4OmDo0aN6nL+6PPlgAMO4FYLmEi3Db00CsJdHAyvKFIkV115lYwZM0awCZ6md7qBsfCWBi14nzIFSGowHON9x40FIzJ9+tfy8cefMMAoYKNedPScck5MyP7N7EJSo0YNamhY8Ltu3TqaldKDHqROlwKoZzizoC/CKQaODhhEYtBILcGdQQKjUyGHjUMHDR7EKBWIIgINin2awi1E5wzE1ESdY1BSH2GwLGN3BSB2Z5Pb1wlE8BXVzAgo2+F9RTUXgKEB6q6oYFQIQcQ1SQUFHGWjAYPJWK3XC2PVnsCmtOFjsnzgoIHSv39/MsACuLlygGZGaV6Aguf+UsCaKaIRhpbCOieY92rUrMF8rPZUonpcBoxoJMScBzRtiUnLli3lhuuvlxdeeEFNgT6aSMqATvBJEgVozotG5YgjjpCZM2fJp9Om8QtUCwWNS4NwJ2WfNR55XffuSlPfK6+8IvPnz6OAwwJvTj9Fo/Ldt99Kr549pV7duga2AcpBkBtqjl9b2YSzvfYR5cwIKB8RrBBQDrFdFA/p6nMIJizC1B1VdW5h+bJl8sUXn0uLFi1kr732MlOG3pgDBuzRmED99ptv5fvvv5c/nvZHFXgQelhDg9pG9h6dwRt68CY1Cmhd0qVcRP75z3/K6X86XZo0aUzmgrVpqAvUffqVopoaBioFhYV0uhkwYAB33n3vvfd0pJ5aIYJUPlAAQgg/DDgRt+9f//yXrFy5SuegzDxLPBvDI8gzNB3TFoTlvPPO4wLvZ5951vmc8TUlJi++9BKnCzAShYZG7cxo6c7HuXzB8iqChgIZwdZ7DipNxojOl8Bc04SXkdJ7AgWyIDtLoV+ZUS0W9r399tuyYcMGvl+9eo28++67nDe67bbbpL6JyZZQ9mLygRBav269/Otf/5J77rmHW7VLTF3KnaGIm2bu62LgBY9Sp4Ct5Ridq6Ly/PMvSN26dTiCBgOBRssWgSEy56v0nE6Oys+gS+kBHK684gq56KKLZNmyZdK8eXMKRjA7auvWBJR6pkHKclDA0rx+/foydOhQ9lMMWlBPECgcQsZQf2avNlYkBjnx8Uvv3r2le/fu8vjjT8g5554jjRs14iD0++++57xWg4YNaTIkWqqexU3ItmGUA+esfurCD7TCwYG367kf+HhqUJqZ8T5yeWeU9bnteez8KaQvaz4Z+w5NEYR34Q6CwzW0Q4cOsv/++8n++/eT3r17yR577EGBhQgB8MxB2a0nWHH4YW0TfnCKOO2006Rho4amglnLCXkWlz54lnq7LI52rA94Z0WismTJUnnxxRdl9OjRzqgWJh93OygORrmfudoXYUejUlhYIOPHjZNHHnmYnqMWJoRUcGSPAqA7NBqcUffY8HDDxo0Cc10R3MbBhMkaEvkD2YVhfGhT0LYvvvhiWb9+Hb37aHWJxWTSc8/JWWedRdgoFevZXTwXz7FtIJfOyX3BjbpDnMSHKd95CihrT031nGiPhOqr84D5cIYGQ5bgIBv32oIJCBObBx10sBx00EFy0oknyZNPPikHHDBAnnrySYZLQWMy7ZQV44AxNIBH0BdffiFr1qyRYcOOd0yGnOOgeSF/aJVctny7R0VTS4nGZGdREbXZsWPGSr169VmH0J44V+RjvaAzxBxCCb0+IZxgRuzSpbOMOGkEF4xawUQBmXIXDxKWlwJWa7XpcA9T3//+9z/Gx+RzZ8ygpnhUJ9uS/qGAQzo4S2Bh9qRJkxg5ZPWqVWxvnTp35qAHbQHfOeAAPMd5JVF04WjplImzp4BKV6LYORR7ThdeNtPHBYU2HP617qS0TcebE0ZF2Nb7nHPOpUz6+OOPNbAoP9HGl4z7ls1b5N///rdcddVVRo4hh/i/nG+hDnN1tdI8fca6Nbb/Dz/8QDB42H///bUKMO9kqhpMRBBuypdyKhhBBALDnMikyKzC3PML85KrVq3i6Jp5Z6L3BzBLpICb7tWr15CDDx4of73hr0xj6wt1yO+soEH7cB1VCqvIySefTLPts888IxMmTKDJEIMOnX+McfE/24Ebhi/tLHv909LDnl0kSOvSW0ClBbaSJIYq73jV2MhZWBmOzc1wHxEJwwxQJEVF2yUUjtEVnZs0UYlSqQaNCmte0CjhyYPFfBiRtWrV0jRuHTWRGaJ9J7bxSkLMHCqGY0KBkgRzYVQQLeKRhx+huz+EFLQZrQrDgIi+PwZ2DkViCHOjVU0GZxYAQwbWqF5N/nbD9TLllZelgBtTJjYIaug5RM7KjIo19aGM+3TvLlu375Dp33wrRZGYRNDH1frruKKjj8MBCnWKtoXB7imnnCqtW+0h//nPfbJs2Qrp26ev1nYsyvplGhMmTTdP9KedZaxeEpsj7Z3G6skBt5/Yewuo5BzLe++2cZU3ba58jxoGE+FapQjXNaBuGJYfTA57x0RjsnbtWm7tDcaD6OOFhVXMQJuz7pQ4XDcVE5m/YIHAU+v444/nczIbwMmVMu8OeNgRgJ3clZDcd+99MvyE4VKvfn0uHeASAmo42gYyXT/ukSfayj7d95FWrVrJjBkzOJ/pZjYq0NxPgutMUsDWDc5DhgyRO++8k7sNULDYjE1bwvomDHa2bNmsc5gxkerVq8npp59Ok/6ZZ5whWFOJz3XQGiNfwQMIJ+RBvpJP/dDVRSw5/Dp7e/G5BUwKuYG+iSD4JAVI2U+SiGmIDefrr76Sxx97jELlqaeeknnz50mN6jVk3bq1MmPGN4xufcedd6jgYTgTYw2iCQAbqWpA2YcffljGjRtHsyBLhsw4TEjMNful3p1yNAtuaV4LyZLFi2Xu3Lly6aWXapXAm5KVQhcfPttl0OgjucCsdG0UgOroGxPsYy8dK6NGnS3du/eQgkLV5DCgCQSUj8QvJyh49cEp6uWXX6bpjjtbF2jUF+wZ9t1338rjjz0hs2b9IB+8/4H07NlTkObEE06Q9957V/bbf3/W35IlS2T69OmyYMECdaJ48knp36+/dOjYwez1lh/8wMESjRiD9kSmX07q7vp5KOZhL4hFi3b9ujxPDOZjx46RcePGS9t2bcuTOje+RRlCwvVK2NnWkgp7MMFLz9ZF1WpVpXr16lJYUMgKcjYThLYVi5oAsyIzZ87kNgt33XUX4TKSBDif0dJyo9CVHwvWozHBYhSMAcOpp5wq/fr3I/OgALA9L5OSyU1qjsDjmcFbFMejjz4mCxcvlkGDBrP9WZNTIKTcxMvstXtQgGvE5sRcEkz1tWrVksIC9fhDR167Zi07NBzR0a9r164t1apXo7YE7apa1apkG9u3b6PTBFUprLGMRslDsDsz96OKN4XMFi4F6IZlOSnZn0IhmTdvHncpxos5c35x3qdz4alBpdUB0PlNHDvlxNAmcpjiXhQ0KBdWKZTGjRt7fbXrc44kYJ/W9RKcx4pG6SF2xRWX0/yHCdLgqDgKROg6HpUffviBc4NYNkBNxrRTOspkEz1X/yBDNG7OI0aOZFy3/v0HxLXubOIV5JXAu8DHEOqsb9++8sADD3BZAOpLdzmISaNGDRPakSVfYUGBFNbQiCR4VlirFoWbfZ9XZwyok9m528HDx8J4z0GlmUky/mmCy7PkKL317lFBNeObGdK8RXPp0KGjiUKRZ0WqZOhqBwvJE48/LhdfdBF7nLbZijeh0YmCHT7M6NpnnnWmfPjhh2SU0PjycrBXidoP6I8lJl9++aWs37Cec9QoHiwi8PRUL2C1vhhPG47TE64rET20cJkpUGYEFHt6IKLQIEEFmATuu/dehvHXEEmZqcwAatkpACbz7bffytq166Rzly5MCMYC84q17pUdmr9f0o4PJMx809FHHS2zZs3iInDMTdGk4m+WAbRyUIAaUzjMANGPPfYYF3jbLTXUra8cwPLx0yyy9swIqHwkus84c7rQmPpgRkKcvvbt2+sgahf92OfMA3ClUgBMBosnr7r6KnpbIYQVNBe4nGex/3niCWEJIQp3d8xzjBw5Uj755BOaIwMNypNsWXuBuUBEPEeYs9Vr1uiiW+aeC60na2TQjNxFxrX7Pk1UvAUUR3A6gc8hZTnvnVGgRbCc6VPJM2fS2DKbLdyff/45OfOss5QBwo0icCtXB5MstQnQG/HTIJToixAT+f233+gqvCcHDSbGnvHqS25H6qCkaS2MaBTCzPy4Fkbho+qjEayNU9MuZiEZgJZ7f+F5Ih4KL3GZAfo3nseJFJWRI06Un36YJdGinfT4czWx4LICKAAXcSzQR0SZ1157A76XThsjOu7qq+zX5GfqxccNr3RDYV9qxXOmXjtI+nmooIp33vQh5gcElBvzBfN+/VUWLlrE8EgYWXCAwXUQaLXBkS0KQDvCbsekfygsE+65R0444QTOB5Z5XgeOP2aTyZ07i2TGjOl0sjj7nLO5Hg6KsRWEO3bslFenTJGvvvpK6tWrJwMHDpIBA/rThAjPTuDjnmlmP3GIkdQ2YiJVqlQ18x5fyYADDkhw5w00KodwWbuw3pQ9evSQ/9xzj4wYcaJUr1ZdpFC1cF/ViKyVqmwZcQDl+WlS2/X8rmwvPAVUulYooungCnNF2RCqDF9BuINp4N9LL70so88fTRd0mG1AEmVODnEqQ5FzugyqjMQYlRxCav2GdYKYaAcPHKimmURZUWxZtLaU+cydO0defPEluoDvuWd7GTXqLPIjaE5YhAmBd+UVV8pnn31Gj69Vq1bK/fffL9dee62cc845Jk6bmkKK7xa7Pg3FYgwsPGrUKOnXv79uzbI7dapia6XiHtoBPDacbNe+vbz77nsyZMixqvSih+9ahRWHrN85J3nxsX/5nYeB523iA4XT+CkTtswYnTE9eHmXXkSw7uGnn36UAQcMcEa8li55V548rj/O5xjBgYHDlMlTZDi0J4axUqFSUn1wsQA8tLC1dUFYOnbqJJdffgUj2oNRQXhh7RveobO+/vrr0rp1a5k69R35+OOPZPLkyZx/xNYqS5YuNYNr4+VpNakE+ho7vnlm56Oww2vfvvvJ4sWLKeSYdya5Q4aYTr6DtRorB6GhkBxzzDHy5htvsAlpde5mvM7lYm5p4lcdewsov3LYHeCQSWhYIzANu30Dtt8YPPgQjqpgEtDK2x0IUsFlhMRwKagOIw+FBKa3KVMmy+BBgziXg7h7pR2QEwBIxoRNC82OxzVr1uIzroFxNGP12rz00rFSt249uh537txZLhs3jt6ciFrhTIS5cEzEARm6huA07+sOzoh+//777/NzlIs4JSYO7rJAAUt31EHtWrVk/YYN8ttvv9PUC0cbaNFsg551nAUkM5lFQh/LXCG9BZRFINVzAodwzfemCi+X07EhAEF7xBjRfOrUqTJk6JA4E7Gf5HJZKgNuqAYXf7eCBUwDHpUdO3ai8AhjZ2RKH3WScBhKcTQATNafvtSddbW+6ZqOIKGGMR0/bBhNe5zbgjcePPFq1uQz7CVGMA6CZnI5IU/7zJxRHCzcjUZln332YUy39evXc5sWMMjgqDgKoP1g3hHb7UycOFGw6SUPd7Uk1G0l4IVucttyxpuq+23a194CqsTeWjrFibdF3qmx0tPFhx359C0anRZWR+siixctklatW+0agYKf5VPZ8hRXoq3OOdBoIQ+g6bz99lty6qmnqjnOeFOqka6UcuK1MdSiqrWe+ZCbWJJRRXWjO0QNwHvuI2W+/eabb5hvQ+yqqpH3rMQzndidf2K/huCDcAIjRBQD7PD6888/M3wO8g2EVCK9snkH2qMO9uqyl8ydM1e2bd2mwaRNa9G6cddtJbxGGzfyAuX1sz16Cqh0yWiGiU4nTBdezqcHgjjMBOLkKVPkyCOOMPdmhG4+yPmymFrLazwdl3JUCCLQR2X7ju3y/fczpVOnjqwXPGfHYgfTR15l1rdOc05U0fCYAkk1MuSFe5wRU2/5smXy9ttvywUXXqjdAlMUTKPjGgq8EmmuWhi1tlCI8c6+++47bW/B3wqnAAZAhVWqcPscLKiOtyRFzatN5etzI4tcXQIlycxRghef1VVTz1ilqvZGjDIq88HGhqIWhGTblm2CjQtHnTWKYU8wyR0/6CYRvw2uMkcBCCAoTzjHYvLxRx9Lj549pErVqk6eMM85HzlPi7lABZu5b671MJ+gXTs/eGlGhRvR0byHdXDRmNx//3/lL3/5i7Rs1YqakH5fTB4ej5yuw8FPSJo1bSJFRTsZWQKLeIOjYilgvXN79OotL778ivTdD3EdbRxOHYxwRFKxaPqXu5udxdQywfKhoTqN1Z/sPDUof8DvXlBQb7FIVH5bsEDatm3LCACIz4XGGhwVRwHLLN57/z0ZPvwE5RXsS5RcZetUtlMaQaV16jJnsPLjjhQQQvjmySeflO7d95HBgwdz2xaHCmk2icMPO1w+//xz5gEHnOCoOAqgrnFgGw6Ycjdt2uxoUXilA/WKwy+fcw5atg+1R/nD0bra98A4jhs61AyddPTuQzYBiJQooCNZaBzYWLJL5866nQHElBUS9lwG+GA2MOnoYDFMMx6FFfeuVIEVE93767XXX+e6qJNGjDB56iZ1mE9Kh2nBuQOuzbNnz6b2Bm0tOCqGAo72HEIcx7DACebn2T+zbXGu0WpSFYNe3ucaCChfqlDDF1lTHnZB7dmzl7PxWDDC9YXIKQGB7IEA+eWXX6Vli5a6kBZOB5wshNnOqkYlgCcQvI8LNdWgFHYkonNOeMb5p2hM3nj9dZk/bx53UoUDDdrGipUr5ZGHH1aNOg2tGvNaLVq24P5BgXAqod6y/Ar9HNtwTPv0Uw4c0MaoXZWhiWUZ1bzJznMOivHifCmGzkD7B88XpDIABKNnkfXr1snq1WukTt06zgQ8MyvHKD0DyCWCpDkKvFnNUHY0b+91bxuTBDw5T0eBHMHCU09EXnjhBYYKgiccFtVSwFDh1XpztKlESsXvQDMDC2m3bN4iS5YsluXLl8vadWu5DxCEBZjUSy++xE06EdLo1ltvJZ0Ruw0eeDfccIPx+isEYZW2ageK51XSlWF2yKt79+7cCbhTp05OCjJE567iLthmXMKf9OZ4QNucG0/7LcqE5/adfV5xpSh7zhZXBIWe+s7bTp9huXOp75e9SN5fGv6BD/QSBTS8JI2BV3EZegooV9sqLl2pz+J4ao9KF16pGVbgB2B6YHDoYB9+9KH07duH9xDK1tU4l8pv+ws7DxDH/1hMNm/ZLCtWriADb9asGdfZIMo3mG4u4V+WqrbtD7hDOGB77QsvvNCEmUJ3wiQUIIEhWooUD5mwXJ+sXr1annvueTn44IHUyJ753//kqKOOkj077ClFO4tk2fJlcsklF+sAwGhwyAqM99ghWBcHw4V2auKhluHiMzdf8qXBAfhgsfB+++0njz76qEBAof5QVpwtg/cEmKEX2p60LaEvbN++XTZs2EBND9ueu4WPRQFp1q1bx0XMTZo0If5WUOGbiiqLxa8sZzftEUB2/foN7EfNmjVn7aGO863/lFRuNkPbffChs/iL3amkpOV+5ymgTO8tN0CbAJ3eMgl9poLKvq9MZxt/DQzimxnfyIknnkhm4QgnePG5GFxFl93wZaKBOkJ8ukmTnpVnn50k++67L5kEzJR///vf6fWmTC+/rMEOQwgJGWDLli2kYcMGatIz3nAkAIjh7mDFVI4Di+wmJo2bNJELLrjAME9ULHRQneuCdnbB6AsE80SgGwcpJgYj7/kMmoJGFikmu10e2QiOgj6lopX5oa6uu+66nGHiECboA9j/DOGe4Fq/atUqbrrYu3dvOfvsswWx66zQQSgwbJsOQdagQQP55ZdfZPTo0WIF1S6EyNEHKA+EKg6Uv3PnTozDeOIJJzrDkBxFPSW02B/c/CxkPRYpilOC6ZXIW0ClK0/Q6e3IFLDShedVglx4Di7PkWtYlixZIl277s1OCObEeSlUZq6V3zQwnL7//ju59dZ/MmZcq9atOdp7+aWX5aKLLpSp777LEXDO4V9qvdM2yXqZP38+zWG2GuxcoVYKpFUpwAytnFEG55TCdJbA4ASCB0cMHZWwFCCFEHoYvqeGHZEQ3Nop6/UbCv+EZQjF4OIIUB2JA39kCRfzrl27yqZNm6R27dpMaJl/MVAy/ghlAaOeOXOm/Pjjj/KHP/yBZs1p06aRYUM4QUixzKGQPPXUUzSRXnnlldTWIdAmTJgg11xzDbeyQFnstxlHPs0MLK4Ag3iJHKiecCI7PllhmvBzLrmrz5DNuzUqH5HNr2GxjwX3ExTYExjGli2b2bEKCsiVmIWLX/mZZdqwdMwPMDH54cefpFq16tKkaTMJg3vGQtKnT1/5bcFCWbtmnTFJpZ1l1gAYcaFzgBISLGrt3qMH8ycDNwLFETilYYZK5E/nRwoKwwLP7sIqCBAbEsTz46+ggJoTNGcIKlgRoP3wmt8XSkFBSAoLC3TgArClCSfg5uSviGKOsAC7/4Zi0rtnD1mxfLlTAjD0ijiQr80bUS7Gjh3LOb9+/frxGt5tMLMq/UUW/r5Q3nrrLTnkkEMEZmSk3X///blE4+uvvlZnExfMiihTefK0ZUcaDPLmLfhNIsZ0Ho1ElEGUB2DwLSngLaDIdcm/tB+X954TG4bK5U2bb98bRjPrhx+kQ8cOhjkZEw7mG3KtPMBXh/o8t2rVSlYsXyHPPvOsFKEzSUjeeQdxBIcKImhT+uZaGUrEBy+1jBDEYJgdO3RUrZYM3JhcS4SRRtvPNFyWTuea9uneXebMmZNQn6bXZf3EXYlDIZqJq1ev7uAERDp27MjBGzQsaJ0fffQh8YMGiAOmMeybVbNmTfnwww+oUdnn/CCP/mDOEwILpk7MT1O7Iv4635tz/KC87RVlcaXBpZvd+1lV3iY+YpB6VvGBHNE3JUodXi6nhOUVjfKD99+Xrl27KeUQUgBDX2ObNvIgJ4pB1Awm6EgHDBggxw87nvMZ2OuoZ4+edJG+6aab2NFQgzoPkhPol4oEFA6uNcL8WjQiP/38k9RvUF/XL5mt1LWHlQoqZz/gnEcoxAXhy1csZz2RERqGWBGIgyFD0EAY4eyel4GzRK9evcis8RyRv2Hyg5kSbRA/4A/nnDlz5pK5W83KDqYqokxlzdPSHuVASKo6derQw3KvvbrovCc5OFomDssTzW2enSxvt6XRouk0BwaEfh6eAsoi4VdmfsPzCy9/4Og8xrx582XEyJFsf/TUol3Wul/6k5MvUMjBFRICkaJDYQ6qqCgiTzzxpExt8a48/fTTUrduHS4wJbPPq2gF6haHQcHSxUtlj9Z7SNUqGt4IgwkwkXw/KABiMWncuJEsXbqUwgDPLKPMJlO3wgUCRTUk9Zy0OEA4/f7773LZZZcp7eGmv2ULmThwxoEz4FSvXoP7qMGBAvDy9cB+YNgWBfPRsSjmHsNqqoXhOd+bn+EfKIYKqfiVz/JJPFtAmWzjJbUearMGcTDqstjaS4KXw+/YQUVk4cLfpXWr1uxspuaIte2ouVUErRt4m6GZzZ37i1SrWlWuveYauXvCBEbefuihB+lcgM6VT/WnDEB7ERwk2rRpo/jb5phL6mwKjQLtjUUJhcjQGzZs6DB8gMt2e7P5WUEFHDDoIZ6xGL35EPkCpmQ+w3qncMgx49n0OCPiB0Z4VnDheyu8UiBVVpLYcgN/XONAqDN4wrIVYm2Xa4CX581PaaqSSQfjKCXnXHWO1k+ie89B+ZnLbgBr48aN0rZdOyms4inzc44K7EqxLpI/UwAAIABJREFUGHdoPe+88+TiSy6R80ePlscff1y2b98m558/WjZt3JR3JgllFBoldtHCRdKnTx+ddLdO2spDcq4+yooQeAP5g2GI7dq2k2XLljnMsaxwMvmdNe9h/g8CBrEI8cwKnJo1agj6jH0GXPBu46ZNUqNGTc5X4RnSWliZxDcd2G7BhGsccJWfN28e56CssE0nj901bSCgfKh5NMoNGzZKi+YtaG/22w7rA4oJIHSUh46kprAXX3xJ6taty23JYX8AQ3/kkUdkzZrVMvXdqWblTQKInL4BQ0OdRIsi8vvvv3F7DaxPUqaujDCnC1AKcpSvYIRYxhAS6dKlC+MMIpmb4ZcCJmOv0b7ww7omBE8dNmwY89J2pzgC582bN9NF3j7HeqhVK1dKv377s/5Yh6YuM4ZsBgCjPHa9184dO3Jq4JCB4mYUZCCg/CBvTGTlypUCuzOZhrJCPyBnBAY6PpgczriAtrR16xZG28ZzCNhu3boJVsIjPA9C9uTbYb2nli5dJi1atDRMQsubT+ZKL7qDCWo5QtJlry7cZRffYrTOevVKmKXnWA+IoMkjRoxwzH3AbeHChdT/Dj30MDpIYAmA1TCgBULADho0yHmGd1aAZQn1cmfDujCak/u6UaNGNL3mQn2Uu1A5ksDTHuVf7Dx1rfQPXo5QzoUGGPrixYsYwBMNlB0q181I4NVRFUZHH320PPHE4/LmW6/LUUcdTTfgTz/9ROrUqSWHHDJYPeIYnsdV6Fy7VMsKBS5Qw7YngrVCBVizpOMwCFpoUu79nHKtGGXFh/ov2lo0Km3btKWjBAceFeTFZxkzBMzixYvllltukQMOOICLv/EOdTB37ly6oGMuql79ejJ8+HCuhYLGXrVqVc5V7dunj3Tq3DlBKOU6g3fj575m2KMNG6V+/QYSDhsX87JWcA5/Z7saULQDWjgf6XIUfxmfp4AyA4KUyRT3VNHipAsvZUSykjAkCxcuYiRjOzrP5fLG6wYtLCZ77b2XPPHkk3L//ffLHXfeSe+qvn36yEMTH5Kq1aqSueRyedxVzKALarmkHgsPMiugbCCWyrCy39Yh2AGYvTXtoay4djNKN30ycW0FEJZaILTRzTffTI1uypQpjqDBN1jjdPnll5v2FBIMjBAB47bbbqOWhdiChx12mFNfmcA1WzBRXjivwLLStk0bZ+CE/MkR3Vw+W0j5lQ8ancGfJyfSiV8ZxOF4CigHg/i35branWLxwY10zdo1bJAMb1SAasvdFugIG6whjsCbqpAmvXsm3EOzkY32DY2DIyMmyN3yuBsmsLQMc8uWrRIpijDKA6fb6EnKErmT5OW1Brg1kS3CBU5oIAgJK5CzVTAIQysUsY7pP//5j5O1FZh4AM8+4Ifvi4qKeD9w4EA6UKDO8KtMB+ILIrAwyuvEB64MBUxmBTYWH4PiJr9Mr8DeAirdfDhMNQ0OsNKFl145M5oaLqTr1q6TGjVrmHmBPCgvmEHMuIXGolKI8EyOlq4j8AJsS4GiQEDlUf0xeG8sxlE8ImFw0GC3cXCN/jLaKDIN3GUxgtaOdUNg8KyrTOedBN/ma4UMzlZIWsGFJBBKeA4hZdc4QWjZb4C7hZWURd7dopxYhAwNqti+k0f9aRfiJ/chc+8MfHdJkPoDbwGFTNM46MlGGKYnpQkvDVQynhTzAFu3bZWaNWoyL7XHZjzbNDPQHgKmQOFkofFxMb4z+VB/wJ14QvCKrFm7Vuw2D5Z5om5KZIIO40ccPYBTOoE8zhUFuSWIfWpC2vCxAUK5DocUvaf51yZLAGjw1gx1UIC/tsfbNOa9216E+gOTh4CyDN5WZbbOyJfFMWcrnNzPcG2fA197QDi5DwvL/Szfrm37whwUBRS1ett+TGVm0CyWFXrZNmkzQxM3P/vIj3MxnMgPsKgMO+q2HdgfuLkIBRoU1gthDRQZoHLJXES18uKU1MygNW1Yv95x94VWZY9imSB7l37BAK8QZI6AQG+kmLFchloZvzbCCvUeNRsa4rn1sNNUITpsgHGhWxhI2qGjLtMWsnG6DT9UWQTUib55CbygEZoC4QplsuYz5mPeBafsUwB1AcELD1jMgbJ+HDScynSeVIqLxKbpW5E8NSjbiVLOyZGwtnM7D1IGmasJwQxXrVrJBkkcMZKwW43kKtKVDS/bvLCtBebOQiHZtFkHDdjvitEwIB8w7wahYMtvLlRoYSt4c0CYQC4YORGKQWxF6flIIQJzFASSqWdqAnymC4T1nREhcJd0hJ1qDI7gQo7IikxN52dUwKgWSCyc5FYkWSxVG8QdJuSxrghOB9BU7CjeFic4Z48CaEugPzQomDXRNmwgCdSgrb3sYeRvTgmszRQI7Zn/TL/xK0dPAWW7QqoZUYNlTQBSfLSXKrycThcOybZt29kgUUlooOnSL6fLm2PIoZlZevPaSBUs+qxTuw7rg+7lxFu/NIY3pyTW1ERBZbQiMBmYbhHxAGt0Vq9azUlvuFFv2rRRNm/ZwnUuW7dsNXNAUVmxciVxadoUOxJDUAgD1WI0jTmJ+vXqczlCo4aNGG2gSZPGjOKN6AmWsWkf11JRrlnhZgvp9CfTzmLCwZEVSvbsFC64yCoFbFuCKXPr1q3xeWkjmpxqzCpWPmeWpUJ4CihnxJdiuSBlHS0ChbGdLEV4uZyMxUOUbPxzmZJyGefKhJu7r7CZQUkJw1NMJ+MRuBfmN24uiKYIV2xsK8KKU40K49qdRUXy22+/yWfTPuOGewhVA3jYy6hps2bSrn17ad26lfTq1VNq1apN8yH2dqqCQLQ0cYTMIEUEEQQAE/kiyjdizG3bvl02btgoq1evocb9/fczKfiweHXHju2MAr733nvLgQcdKG32aEMXfyBAgcMMKDlZdTQ/YoNArO0KF9DpAIwRQs6eK1Md51tZUA8YlGzbtk35gruR5lthkvFNLou9R2fxmf95C6hkpIL7slPAPaQve6rgS78oAD5u4r6BueOwc1B8bsws27dula+//lo+/fRT7qkE81jz5i24S+2ZZ55JTade3Xq6IzzMNAiAasILKVRF2PZPSjNOFKt5h8acUFhqGK2auLQ0haS5UaeAMXcELW3J4sXy66+/ygvPv8DFrhs3bhAIrH79+kv/AwYwmC+ELSLQh7h7rQpdQATuMPHBtdk6I5icglOWKWA1YWSL60p/uPmdu2P4UHBvAZV2Ri4AuHTd+oB37oFILl/yfe5hXLkwsnyAdNf5G1vAiPUUi8Vk0eLF8tm0aTJ9xnRqL1337ioHHnigjBkzRqrDzEYNywADc4HrNp5ybZtqX7iFaIHsw5fIknyIF8ZBgoLR+CBRC3IbEcyMMhA0+wdhs74G9etTIA0ZOoR5YvT9xZdfEN+HH54oTZo05WLw/gP6S8sWLaRq1WpcKgAtCodljHYOypY/OGeXAtbE6ggnNpKAIaRSC94CKhVorjS7Z3UYDuWiQ3CZRQqYRkd+YNY9gVlgS/QPPvhA3nnnHSIz9Lihcu0110ods9+VkUMqccxiXoodo30ZEWQkEsILWW8LnFVEUVjRScIING7xaBDCiU3DmOg4y2yEX1idLcDMbPxAalohobkQC1kHHjyQANavXy8ffvSR3HrLLTQVHnPsMTJo8CHSsmUramCY48LB9Fkke5DVrhSwdUAhZZqBfmVv0G4qy8HGnZHCeAooTPandTjJ9SJteGkhk9nE2hjVXRgmJGfklNlsdx/oTluKF9k6o6CZ8tp45VBQYDFoURHNZG+88YZ89dVXMmTIEPnHzTdLs6ZNHU2D0CiEQhKGoKGwUa2GqlE8O5Uwhqdo/ar65G7XVrC4nzkgmNaoXJox1S+bRjW1eEHRjvQDPUGLw5quYccfL8cffzyjfn89fbr861//kjVr1sryFSvkoIMOMh5j6sVnNSnbHpGXvXbwCi58pwBoDFojOjs8+bQ9aN3qcAZZxuvadwQyDDBeBs2IbdgMjOy1Xyh4CijTF1POJ9GLT00hKQPLg4Qwt3BS3uwHlS798qDI2UNxF2KCAZitJYzzQ5EJ8bNk6RJ55n/PyI8//SRVCgsZkHTcuPE6bxPWwLHoRAU+T+amTQyWEb6FmGfWAsf/JjIz4N+kWTM59tghcuSRR8nixUvkggsvlIkTJ8qee+4phx56KOeiMLcFTzJ8j58VWGnjGgAoEwVAcxsxAxxQa7dy8ELbJdEyKZAtRewLe5/m2VNApUtGuvEmIJtwkybauZUcDREhdXbs2BFfC7XrEDy3kM43bFzNh50C+NPSpqFz5v4yV5595ln55Ze5MmLESBkzdqx8+cUXdIJgUUMh3b6eEc1dwCwd8MgCTpQH9gsfz8Vk4BZKu7x2zVkZhkAJjfh24TC3ecEcFjadxP5L9913H3cRxrYVLVu2pGACE7Huz4EW5WNVFgMK/AAH+AH2hcK90tw2Mrwtpg0WAyvXH2mJjKmby2v8LZe3gEo3n7gKpXWRLrwcrim4LaMhokHWrFmDjDCH0c071NjhXUwb95YJzJ0zRyZMmEBNAZ533bt3Vy+2UIiLV+EdZz0ZItEIGXqxBLDwcc54W03OAJlaBCx2yd/Y53ahsTI9zFvRrEkBHOZ2Fr179+a+Sy+99BIZIzYM3GOPPQggzizj8IIrfylgBwBYXsCF09gs01nd6l2v/mKRRWjGcp2JknkLqCyWL++zisWkdp3asm3bVolJvbwvTkUXwDJRno20YPTrsJqrgB/WK2Gbhrr16lJz2HvvvQQu2AWFaNLqqFC3bh2Bq7Yyf5j1dFddzlnZ+aaKLizzT+raSbfJKIIB0rOQGlSB7IwUcT8l0AtmPGhKbdq0kUsuuYRu6++++y5D7pxyyimCaONuTcrSOjmP4D51CqB+YF6F2z+8LZ12bIVUVgZBqeNfaspd8NfWiGZbStMtFXTyB94CyqipyQnKes/xoJnA5uAwTXhlzbeivqtdq7ZgewdUkDbIisKkcuRrQwVBmICemEvB1hlr162VB/77gMxfMF/OPedcwR5CeA/GDOJjAS4YBBaJN27cWJYvX27MK0oXCidcVoL2iD7Gn6EPy+0SUqAL5qTatWsn8+fPl6effpoCCg4jdevW1XZqJvSRNjj8oQAGADaKRPt27bU9crkCueKuyrI/2WYPiimGkyH5vPI9tDk/D08B5W8+aobwE/FcgoVKadS4kaxdu1ZCoT3ZAP2tplwqbfZwwT5bOEDfHTt3yquvvir/+9//5Iw/nyFX/+Vq3R0X0zOW2DGNmA0GAUcDOK4UFlaRop1FuicUgeU/f0iogZjOdWDEbg83k8A1mGXHjh1l7NixMmPGDLn77rvlkEMOoXDHTrbB4S8FrAa1Zs0aadSoIQdNjGJCU5j69Onqb3/zzRY0HYRnJzdPAZXuiIrVwApR99104WWHHKnngpHS6jWrdT6Ag/lgRJo6NSGUovSKRDuaN2++/P1vN8oBBx5ITzU4BOCwflGYAwQjphIAIVWAiLB6X6cOYvFZVSNug7AmsnRwrLi0KpGtXMZeZAirg8MKJ/Q3K5zwHAIMWibmp/bZZx+ZOnUqXdQxb4ct2IPDXwqA/hiwNmnalBFIMCyyHEHP9s7ffLMFzY29bXOat/tN+th4CiiHminmwejPztA2zhhSBJfzyZq3aC6zZs6UkGGO6dIv5wvsF4LGPJCs12AtLGLXPfjAf2XuL7/IddddL506dSKTteGGQGMGgTWLcgkD618jEE7YbFFNf9vhvFKjRnydU7p9yEoGNw3MGlw8cgQihYSui7OdmAM1pE8HB0ZWN5nHovLb77/Ri9QKJYuW+966mOMZtKZjjz1WevXqJc8//7y0b9+e26/DJRrv8cMBnO2cln1mYQfn0imAeVM4SZCa8UZResI8+4KDPeohiRFc/ChGxvaD8gO5vIERi0mzZs1l4cJFEosEC3XLVG8Ok0dkhqjupWSeQQDN/vlnGT9uHDv4hLsnSNduXWmqKsCeWwjMC4cH7J3B3o+EDkAN2Gs6DNz/EYWcWhYXv8ZHsmXCs7iPkCcEEoLBxqL6wwJtI3eAP5h7FCZKs15L57yYyCzcLA5w2Z7ROmHKi3L9/PPPXPeEPK0gLAkShA2+g2cfHCmgfd1zzz0M/YR0Fg6+g7k0EE4lUXPXd6AfBPuKFSukNqJ7GIHPLxOb6q6J8+FJvKs5RcoU2t4aVBIS5UfABaAyVEoJBACTqFOntixbvkw7s6voJSQLXkF7Iq1UjYqA2Uci8vzzLwgiQNxwww2yZ4c9HaaLYK06GoVwMuSztLb3FBJmM42Y0EHgx59+JDNWoaZu2mkzXeQHtBn2yMhH9CbgA+Fodu61AkPDGEWNhm2+S7UFmDxAPCxQnjtnrnTZay9CA2P0OtxlptOJcSg55phjaPp75JFHGI2if//+FFrAHWns2Qtu8DyRAqAZt9kIhaS6XQdlBhTOl7bdOg/y7CIZf9wnP/OhSN6tOU3gGcA1TYwylxwaAExIC+bP59YKOsLNXH6VA7JtITirWQluuRdffIksXrKYI3p4oOGgGY/CzMTBo2Sw0g3pVcDF6aIwIShat24tM6bPoNCARuMHs6XQMV5EqGvUP+Z48Jx1H4vpfVS1KMynqWQ1wtHexBFO+QrM8Nd5v9LEByDErYzQkBaCCmngfj5+/HhuUQ5BBQZr4eG74CgfBeA9ivZL60BEg/kqBNNeywcux79GmTJzeAoo7Wqp/yW6LrxTh5T7KTE6RkfHZPPixYu06IZZ5T722cEQQoQM3NAFYaGK6KWnI/Sff/5JLrjgAhk27HgZd5ma9qgNmEXq1ErAJw2vtN08fnbB50MVWm3bteWaqShNr+pMYQVJuUtuTGhY8AvNBfW+eNFS6d6jl7z66uu62y5qP4S9qIrk4YcfkbPOOkcuvPBiOf+80bJkyVI6fujiWu0cxKGMbUWHqKbERiZv37ZNNqzfIDVr1mS7gzApi5Cy37hNeJiDOvHEE7nYF4ufFy1aRFj4BoetP94Ef4qlAOmKqPm/L5S2e7RhlWGRLmlnjLtag+VufUydE6mS2isIgb2o+eMeZdq2iyVQOR96mvjS9XICIS0zAU7pwitnubL6ORgpGmCXLl240V279ntya/FMqLxZLZjPmXEgbgQMGCmERjQs8sGHH8iDDzwoN910k7SH1mQ88DDXVMB5Jp27KTM6Zn4Ira5li5aMqlAUKZIqYQ13lJI+YIWjq+9hF2VoHdiEEAKJ+0XFomwLjz32uDz11NPyyiuvSO3ateTBBx+U0aMvkP/972mpVaum6RvoFbQHlq1owMEIbKCB2zVr10rrPVo7priSTHxemaDt2jYMYdSnTx+aRKFJwfwHZwo8t994wdndn1M4GSIsWbJELrrwQrNJpppKKw19kjqQ8npO+vo+X+mpQbH1206ZwjlBIKWQPt38s5oefCMak4MOPpgb35GL2IVklb3s5Skfeigtc8pl4WDwyCMPc4O++++/X9q3b2eCumpjp4C35qVy5MMOo4oMO8zeXfcWrEkh87bmtnLAY1uyuJvBFpgRGPgRRxwh0KggTC2DWrZ0mdx88y0yatQozk3CxDds+HBqci+88KIRLUYwAQ8cZcHHfMqPKShDjBTRvFlzhzFYbcf5tAwXHCyYDR5hCcDRpEkTufTSS2XatGny1ltvET5gl1VDK0O2lfeTmMj69eukQ8eObBPY8bhM9VuWNpCL3xj1wzZlPyvWW0ClmwuxzQTK6SLmf3q2mZBIjx495Ndf51FYYatvMizXiNv/nPMIIgUTvPXgCIFzRO666y5ZsXKl3H777VKvQX0JhQtoKgUTxI8H6GeFfRmL6x4chQsLpOvee8uC+Qu0PqjtlhFQMZ/Zuv7yyy9l9apVsv/++yuaNP9FiSsWFGOzwd69e9GZA0y/SeNG0rBRA3kZ8fEY9cJVvmLyKekR57TwQSwms2bNko6dOjoaTqoCxNLbrpeCMMdWEeeee65gHypEoUDduRcEl4Tj7vjOtlsMkOBhCpMpeIAduFRemuiQMBOsLjMCymEqmUA596qZpQyFpFrVanSScHdikiL3UM4ORrbwEE7GSgetCUF1//KXvwg22Lvi8iukeo3qHGBitb3t5GSYlAZGFSonxpbhYikeTFbffvuNuqXbBb3lgWebsTEdrt+wQZ555hkZN26cRqigQggzrwKdOXMmgwfD8UCFiZmjbNlKZs6aJZg3cj62ZSwnPoALtoC8mjRuwtRWe7JlLw9IfIt0bjMe7sFkR4wYQTf2xx9/nALKwreM157Lm19l+d5dflwvXbqU1gCWj3ET1XJQWcq769SFDgnNkMvXYnoKKBA65Z+ZDNSCcOicOqx08MhmWmMiada8mfzwww/OhCZry2hTKdMzm+XwKS9lwGCh+o+aUzQqmzdtliuvvFJ69ugh55x9tmMy8pU2akd02twebdpQMMCjCrYWrlOCezgkShnLC/yBIwYfN/71RprvargdE0x4Jcx1rVy5ksIX64tUW1ITHjSSLVu2yLp168ixLB48lwUPtqOoCvuYcBfdn376SWrWqukIdrQ34On3cdRRR3Fe6r///a96qhoXdL/zyUd4VmCjjUBbxgaZPXv2otkXIbds2/G1jZelvVTgN37Vo6eAonBxjYDLfZ+MYTqw8iCtZUR9+/SR999/X9fHEG/jLJIHZSh3HZdQJi16TM15kSh3uAVzvmTMJZx4/+Ppp0uVqlV10S3MeSXASuUdeTTlT0wQGmnF8hUMPYOMlIHjrNmWCh/oxWKyc8cOmfTss3LggQdK167dtIWbPPAenn1gVriG5oFi0bXdLBDWfBUWiptwlKX8TEBkqHGCESLGXmGB+jpZ+JZhJsBP4wbwwGQPP/xwaqNY1IutJJAfnvudXxqoVkhSS3cIJ9Blzpy50r9/P51vLQ6jstR1Ln+DMrnxK66MPj3z9uKzcwApZxQz8RDVhlGpGzGKCDkUDskBBxzAgKbhgrE6bDZ6b6Uuf3FthNUeEgQcgtYBs9bl4y+Xk0eOlKOOPsph5HRc4Dqo4oD48wyMo0+ffbl5IZwaWBf0UbCVU3I+1AFjMVmydJk8/vgTcsqpp8ikSZNoMoRDBOBBWMDhcOjQodKocWPZ8u33FFjhECbIVRgiEjtC3yDKOowiaC/s6CVnr28Nqvge8g55fvvtt2xvYJCZbF+AD20Q5379+jGve++9V84//3ypXr06n2cy/7KQpyK/QRu2WhK8OREgtgU2iuRgBQv5dJsXjirA2G1dViTSfudNvybX3LFP8L01qLQzqIy14EEUjsTR8kQaNWosDRtqZHNwHzu68khZKR6DgTsHeW48fBHmnnbu3CF//euNcsyxx8ixQ4aQwaF1YAEuGbWT2McLV/PD5fDhJ8hnn33GDBwnA7xwfeeVOy3sMZFNGzdQwLz5xpsyZfKr8uqUKQy6CgYFYfHWm2/Lzh1F0qtnL9m0aaOsXbNOYpx8K5CinRFZvmyF7Nu7t9mzyuRWhvzdeFFYgvGFwjJz1o+yZ4eOpH4m2xmEj4WPskJIIdrEY489VqzThP3WjXdlvnaXFwt04RyDRXFYGSQh1yJdVzfJa3oktVnEbcFcbyaK56lBlaXjlkhkN7ZlZAQlwsvxlzpNSJHE0frM72fKwIEDdQ4CVZdUqTlenHKhh8DALB/qHGYfrJzn5DDMYjvlqquu5tYOw4cNZyNWUpg05cqpjB+72x6ThKRTp46MNUeTVDgsOjIDJqXXDRgQTHZdu+0jzz3/HDUneKsjG8w3HnnEEXL+6PNlxEkjKHyxdujWW2+Rr6d/zVBLiK6+YsVKesOdcOIJgm1EVHtyNQrX5S6ltOUxZ4zMly1fTk9B+222NRgIqE2bNskTTzwhZ511FjUICC/QKtu4WBpU1Nld5k8++UTOOeds09+VK3AAl7ZFqqJK55Gvu72a/u9+5JGq3I+9NSh0hnR+TGzwSQdOHqR1d0hcDxgwQF59dQo7LShgR+Bp0TOX6YCCAT86RFA2UVBhfRDWNyGaw8knn2xfxIV1pspkuwGEpFmfhJ12GzduJHPmzuHckKJr8C4ND1Myu42HnbtCXUPg0ZTjWiOEiCLjxo2XiQ9N1F2WI1F6/e3Zvr0MHXqc0wwUTWJScl+z5UFbYp4xwXbuWBgOoeBuf65PM3oJpow5qUaNGslTTz2VkBfe7U4H6I8yw5T9+++/S5fOnU19ugY/pbWxfHqPynXja/p/JmrdW0AlYODGpmzXuyJbtnSJJc+PNPQOc6HaoUMH+XXePNm4aSNjcakJzPVBmrTNNRopw9Z5Fkgfy59eevElhn666MKL6I4NOjECuWH4NFcZTyM/y+TANWuuYNKDIDnssMO5KBjXiiS/TOptu9YTRoZgQAhki1jogIfpI4lFcMdo5hCE0VjEzDdFZNSoM2XIkGPlggtGU7tatmyJTHxkolSrVlU1TGRjBHppZUfe6umneOP+ww8/5BosXGf7sHnijN15Me/y6aefEo2KEJbZLr87P9CAWnkoJAsWLOBeW5hn1EOtCVaPKq2e8+U9yox/Fl/b/9Gn+M7HNulp4vOl2buAuC7d9VtJrtVcZRkZdnHFZPz0r6fLoMGDpICuAlhjAnZWCY+QbohH5sTo3iH58osv5YUXnpcnnnxSqhQWGu0JZU+igLELJD31h0hm4lZiMOmFZMABA+S+++/TsERVzE6ydn7F4OGVcQLjheIFG5+IdO++jyxZsjiezIQNgvPAZZddGn+efOXyjyi97Cr8sYYM2tryFcu5iBbryCricJvy4IBy2mmnyR133MGAtdizK4FWqPFKbPazZYWQwpq0U045JV5eLjhHiy+9hiuiHtPNE3KolG6TbhbGFF8MGEj9dP4RpAv7dGDlfFrOt5Ab0qCHDjlkyFB5//33jDZh51tyviQp1Tn6H8K5oNxosiuWL5c77rxDJtxzD+du4N5WoSWH/T+CboppAAAgAElEQVQk9ETr3au3/PTjjzoHxPapcyblwo+MJ3FRMRhVuX7loAjph0XMhh288frr3B4DfQx5Kt2L6cQZfGTzRd4QUhdffLFMmTKFIaXwzh547763zyvDGWWz5YOAQnBd7FaM8vLH3oCmV8n+GX7HemVZtYycdzZl96t+vU18aGNp/GxnIqJpwEkHh+ymNZ2SZUWQ0uYyf8ECWbN6NelIelRSOug8DzbsC8nWbVu5ZcZ1110nDeo3oEmP/KoCy67sAS0xJEceeaQ899xz8YEDjXRmKFiBOJbUVkk/oBgKCXYHnjx5Mtc/4d6al/xiCKnAgUYFbW7kyJFio00ALxwQXmDilfGgEDLCGNrT3nvvTc02XlzboNLjpSW1jQp5h8q0RcMZN3YM7nNFewuodDOyiKcLJ2/Sm04IbSKkHRPeXZMnv6LzB1Az8In95U25SkcUDAgMCSaoe/9zL0Pj7NNtH6FTAQwc8R5bOrBMfKFrWwm52z7dZPbsObJ69SrFORLJRI6+w4SZCIt+EXuvWfPmUqdOHWf0XlH0dTNo4NC2bVt6ayIMlD0qCjebfybPKBt+aPuIzfjnP/+ZArmgADs9Z4hjZ7JAqcAm21PeZjhgKlA803gLKMtI0zoblNOC4WLquQwHJAZ+HFloXLY//OEUmTZN195QPnFy0dRFLpelDLhB5ujPFDom8s7b78i8efM4ktb+qXo0/5YBpiO8ff4WTARaHmYA4S4+bNgw+ejDj1hhEKqZytcvuFhLBc/9WKhAXnp5shx66GFkhLZXQ1BU5AH6QovCgSgbCJQLjQKH1aR4U0n+sD0ZmoP227ZtlVo1qkuH9u0khLVPdKUx/MCW2ec27VfbShuOKa1daWKL69fZU0Cpn0Yaf51RM2oGVVa5/9GDBbWNlf4m5E3VatWkc+fO8vnnn3NEBQ82eLKhgef9P3rIqfaB8kAjwfYTt9xyC51BtIHq5H5Fl5XtD84bYJiRCKM9QLNFnXG3Xru4OFdqxUh/thM7zyEiq1evlunTp0vz5s3p0uxmlErvivkLJk0N2rjan3rqqYKI7ohJaAVXxWCWuVxRXpQbdYCyDj3uOEEcRh5kAxXd6jOYfzL/Mm3U3V79oryngPIrg90FjrI/LS06JWLzocKwQykCbEaKiug9hi/QdPL6sBoJdo7dWcRIEf93000yduxYRlqIT5bC1JEDJTWDJdQJ4v81aNBAmjZtJh999DHryExI5QCiJaOA9UaDBw+OT8JXkINEMpZWUFpNDrv7Yj7qhRdeoCC1z5PT5eu9LQ/KvXXrVm7lcthhhwm8d/GMo9R8LVyO4e0poHRiOY2/jtlBOVQakPLHBwYeLJiAMmWHoOrUubO0bNmSaySsm3ne0wJB54ygxTwTQv+0aN6cbtwQvtAU+bPbZ1R0DXJX3njPQx1deNFF8vIrLzv1lVN1gvZjvKHADOFavn37dvn4448ZYsgySJTIfR0vYXavgINbSOEelgMMBBBZoTIelu6YE4RrOZYVYKDD56i7yvwvuXyutoryW9r4Ue+eAsoP4DkxevalIGUEYgZPnIaySWIxGTFypDzwwAMSMWYB+yqvzq5CWf0PDXHZsmWMyXbRxReTSYGZOiPIHBpMuhkGFNg2bdrQvDd37lzijbkot1GkYutGKQymjx/azZNPPUUXZpiWdJSeG8LJ0snNlKywwlwfFvBu2LDBwdl+n89nWy9YoPzBBx8wOr+zlxkEkzM4z+dSlgd3tQlZvlCelKV96y2gLENK9ezOOVUY+ZrOlB0aFBrzPt26kZHPnTNHt+Fw08Ze53JZgaMRNto5sX1GhL/77r1PLr/8cm5pURAukDAW5eLI4fKwO8Vi3C32zjvvdOZzUDar/VYo/mZkR2EkItu2bpV33nmHDgi6jQeIm7sH6AjmXaNGDTnhhBPkySefJLKkL5qSMbnmbglKxgwCCD/MBx566KGMTo91gCqYjPdQDrd/39s2tcXMWPO9BZQd/aZ6ds+zpAojX9ORf4Q4IQ8hha0KMD+DOQQwRzCehEaC/pDLZQV+STwRZrLPP/9M1qxZLX379uUH7KBmvU5ul0cZTJe9ujCW3K+//Mo6AeO0mxpWKP6m79hR+euvvy7d9+lOho94b7nO4NEO7OAM8QKxUSM2ViR9rRmsZBmQ828hgL/44gtuXMnuYQWS7di53J/9xs3MqgOs34e3gEqzh+6KrN9UyV14iJtmzVwcLIZC0r1HD1myZInMmT2bIy0IKftThmPT5OiZA0M1OaF8cI6477775ZprrmF5EPrHMiBl8jlaDrRr44WE82mnnibQolAmMH8VsuoqXGGjBqKI9hHjQm9sa9F/QH/SV0fpfrMBf+G5BSiuTzrpJEaZwGZ+wJ8DNH+zzDo0mC6x91vdunVNu6dqmOMjTf/7pBr3TNld3nx+VYi3gDITtTR5lPd6l+E2Z3PVfFJeWHn4vTpKCBeqFhSGOZosLCyQSy65RO6++24uuLSdlMKMoy/jXJGD5WWztuYvLnqNybOTnmXU9pYtW7GcGDEDdcxBMSBsDpYj3pZ1LyqohdCiEAXhy6++VEMFCovlAMZSg1uqj5ksj+kvTp5wOggVcM+n5154UfoNGCBVq2rsQDD4XBdSbhzRLrCouFu3bjJt2jQycxtdwgoye/aLqfkNB/jZH/pt0c4dMmP6V3LeOWdLOATHCPx2Ix5ntUTjCAJ6I5gZf8apx6868BZQaeaQZBFKE1q+J49JuKBAevXqJU2bNpHp02do1bJV59ZktyelDa7oqNgH6LVXX5M//el0Kvesa3Ly/Kh1y+Ch9RUWFMj48ePl4YkT42ZXlxs9nCuSx1ueNEr5BaWiLibmglel46pVq+TNN9+k5x5Ag9njyHWGnkwG0Puoo47ijsbQoqymauvBnpPT5co98LM/1AHq5LRTT5VatWvFlexcQbZC8Mhcv8+MgCK+mUO6QuogjUzB5GKRqGB/pFGjzmbk5+07tnPbBWhbuc5wyEC4300RO+rzLzwvfzjlD1KvXn1qF9SYQB9UeZ5UO2hewHUrIk2bNZW99+7KrThsXfBcAeXRKOk6Yv/nP/8pgwYNcrQnjN6BV64z9OSuAo0JP+yT9sYbbxB/lCOB1smJcuje4gmUsFh64cJFMmToUFqEKLi490oOIZxNVGx/z1BfyYyAyiaB8iAvtRph4rhAWu/RWg455BBuFw5mZEdmuVwMy0wQdQHRAbDV+TFHH63ak13rhAaKgqoykMvFUSZPD8uommHDML9eLK+88rKsX7dOHSaicQbKMmWyRDQfqmZEE1JRkXzzzTeyYsUKat2YkLdCyZ4ziY7fsFEmaB7YhffHH3+ULVu2JLT7XC8T8LN9ABHboXHXqlVbCqDRuuI8+k23nIbnEkhWRmUCX28BZZlNimd15XWhnCIch+nlcXpWICcYNOL36aefLpMmTZJly5brhL0dTTqOCC5mnwPlxjwZND0wmsmvTJY/nn66IIwTOi7sznrYc9lwtx1e510gDEgKCjiOWF3lVtLB+9EIDfsxv3FNFrnSlNRudE2UzkOxbPQ6K6B2e+utt1LTRWBWcJ8o6gbAygi7/N+pV6c6lqi5F7Hs/va3vzFmIGgL7QNHWRk56aeVwr/23tLc9cq5tO/s2Xnh4wXKgcEZ1g5ZnADefe1jdr6AsrhBwGLQgCgZvXr3cowFti2Vv97L1k9yEi4rLY6/bTN6Nv3YF+pjbsvjSMxUGUN5npGwLIMykPKkrZzfgtCwZYtUr1Fdxl9+udx2223q0QQSwXwDohmmm0s0AOZg5Js2bZT33ntPjht6HFuNZaqp4BrveLZ9wGstwojoyfDodWeEEvCIRNTDjYtrNbkzwk1O63lvEADNEUMNETEQRgiwsb6F1YA6YZRWZaIqqsrfF4rFgbWtghntwsrcaCTKdUO9e/eWJk2aqDaHl+U4IMisORB548A9Drc24MbLvuNHPv9BPtACweQxD/v1118zRJDF0efsfAVn6YWQRoiKceONN1JzYltg2/OpPbgcMdz1kovXtj9a3BIJzp6T+CiNO08BRatDGo5lzsCayCljThdmPqcHA4SjBOLBYWK+z777SsNGDbm3j04cR+OLeNOgeyZoBKkJBvPyyy9zTgTrumDu+//tfQe8VMX1/9l9j16lSpHeVBQV1CiKDRVLjFGjRqPGHjUqoGIBTRRbNCqIYo8tlkR/seevqFijxtgVUQQFO9hBEIG3+/98vzPn7uzyLrzde3ff27dzYd/tZ858Z+45c2bOnGG8QYjyPPkN6qs1umClIFYhKjyEGISCmw9cx6Z7HAdRyHGSZ/qkbdvA8DrE5FekW92kiYwfP16unHql/LjkR9NgsKsFkwH9U0h6zjvZ3wYzRuUM8u+9N1seeOABGTVqFJUKrA7gkc+mOLrvKK6qqNx7eB5p4J4KZPd+1GPQBMZwjsDk3W222YYefeBJ046aRpzvaz3DHj/gcu+99wqC4CJ8U1Z7AUXjlK1bbxvrMbB28xYn9rm0QhVUFgcuN3U8Vu8n3UelV9bvs4WctiLRtJarqqtl3Lhxcvfd/+C4jqnkiOVnBHTDy6/QekL3JHhFC9J0bxgPp3z4RXchhBZ+fE8SsmLFSsabCwSW3rPKasXKFbJo0UKu2ApBl/lIHDrOO2vkh2Drp2AkDIQlctW5S2fZd7995corpwYKEY0L5Vf3a6S/Fj6UBvcOFogY8Ze/XCJHHXUUu/UMT9mKWble0x50sQFLYPXdd9/xh4YQFEXuBiW4dOlS+f777/nT93OfK/Rc6WEPfuAsAStV50WBz4a0Kb+q1N977z3Od9p7771tAwqfQKYO8/m1lHmU+lIO7wID9xdXea5eW+Oi7OlkEIAcpnpyLqUTnH8z/pTxMmnSRE56ZWuZYx54Dq3aJKQMFULmzRIc2Z5GiDkqDBF57tnnZOONN2YfPCqi6eIo3KOM3WqJKpk370O56cYb2X1yxpmnyx577sEsszVvFcnbb70tGBvq17+/fPrJJzJ48BA57bQJkk4n2RVnhIUVcirrjIyuHSy9Z/fcwYrAXI5EQvb+1d7y4gsvcn0rrMBLXqqTMNusQg12tdOvw1V2j0KosbzNvKfLrpgiffr1l46dOhvlbelQANaBZu4jiIGHGJCzZs2iYsAyHZg0iwmmKFf8IISxwjBiEvbp04cKCtMIjj32WEamVyWZS7uQc80HxnF69OjBNaOGDRtGUqoMCqFbjHdUaQLDJ2Y8LtdcM11Q21DzNR/FSLcsaOr3EzBrmqv49PTzC25FPAi3oDS1Qvcuq4XSaKTvURCiVS4JGT58OEMF3XXXXTxHYFAKL+SdGFptUUIsUN24oVWUTJpgpX//O9dR4odrQ9nohGRls6570EAdR7chfltsuaV8+NFHsspZ3RZCAG75X3/1lfzhD3+Q3XffnY4D06ZNk6eeekpuvPFGOjDgOWswWJ7Nrq68BM+p0uV8o4ScccYZctvtt8sXX3xBbWTybT4Xo9AyxRPQqHMZGXzZrWmt66efekref/99dqFGFYDEN5GQ22+/nWtHHXPMMbL//vtzIUEs/YJ0YMkgHYyrvPHGG7TmEZUbzyL6/lVXXcX7zLeFtNCd0lC+sN9tt92Cbr6GqJzAEzBC1x56Ojp16hTEmcyaVgFQ6lzujfRZJ1uF1pGw98IVVETU+Qma79CmXemlmJ1/GEZsdyQScsSRR7L7DLHt1NCikrC6qdRfABSnCV1klOUXn38hbdq05hIKHHcyzBvrjhZAdt7Wzq+tEgmRvn370jLDFViQZlPPtrRMmTKFbskHHXwwBQaiPmCtoenTr6bywvNGoQMs+yug7tKbD+BbzDt07CinnnKKnHnmmRTspmDsgDiZzDfPmecpsK3yB84IgXXZ5ZfTukEXnAp0C0ZBO9AEtocddhiDzP7yl79kPEg0CN58882gqw/HHTt2ZLw8WIoQzIj0jukE2gVXEAPOS6pwsUfeIPg7dOjAGJVLlixxnmw4h+AR3oYbbLCBtTixpDHKEJstSy1SPa/AfdCYtd8ezoNrFq0ou1AFpdgXumdZBYUZFGkFFuHqeafrMpYatx8snCYuufQSgXXw9aKv2KUEgUkvNetaXWg5FPaesXCw+izenzFjhuy11684GpxO1VCHajXEfWz5pGM+dDNwDscE3ZAeaWESbVUVF0J85tlnBQFHoYQw7wQCDmsNffvtd/LKK/9jQF4oD9VNwT5fnmwOIETRQoagRpcmFqK7atpVDG9D/iikzCeYT57dZ5lHeNWl07JyxUo5+5xzaOG0b98+sGwUk0L2yAMUEaI3QOmotYRuNSh4BG/FdWzwFHzttdcE6xqpIsGYC7wIEV4JeMehMN18sCs7kaBH32OPPRbw4j5Tn8fAAVYm5qGNGzcWLjnsSVAFZTBB8dkGi23UuGXcmI9RNpo/HvObsCXm3oihEEMVlPlQswe+6nwNIgz9IOwLMcd1fpcCosB0y+hdjHUwdlXSePd16dxFTjzpJMbrg0ur1QLsxoIiKyV+ptIZV50VP/8sjz/xuGw2fDg/SHgixsFPFbwaE/BoTAqOuSGfrDampY2xEIw5ocsJ+YfSwK9Lly7cQ5Aai05dqBFGr0CsOOkyYeIK2rEhpIlur8WLf6BnHQQ9Ghf8OrV6K8drKCP9ToOuQbxDJVIjkydPlj69+3D8R/Ooz0fZr7feerRQQBMKAcKU9UpE1l9/fVOWySS7bfv3788pD0888QRXwW3Xrp3QGcYyABpxbUoLChIu55i4i2MV9nGlUwgdVeYIMYUI8hgbhsdqVZNqQSxN1C0Ta9IsTMq6hvpWaJ1bQ50BTg31B+G0Nt4Kwb+2d0IVVG0P53MtviqdT6rl8Sw/0tU++rSMGD5CDvztgXQIYGs9IWa2eomzBf5gI0BdvPXWW9K5Uydp364tP0TI59VYL4i/1WuIuZKp/N9++62sXLWKXVDatQhBxtVLJc2JzrCsiCd5WJ1mIayhEYiAsUgTAmrixIkM0YP5O0yBitQoGSAVaKzQxIAk3jTCDAAiH7f//e+ycNFXsu2oUcwDrkEBYx/nBsUKulDosAqhkHC+YsUKYjl27Fh2ByJq+pw5c2SPPfYIlBqei3tDeYEusIU1jHE+XNNyjDv/a+PfTQ+Y3HrrLTJ58nkcv2Ndd8vDFOPaSFbY/Xi+u9pAi7/2IRXzFdeWnr+Wg0DwYaJbqapK9vrlXvSe+tvfbmbLEl01pd74wdJQSHNF1EMOOZRi2AiWOGK7WAubGavli3fqOy1NR0iCt5UrMelT5wcZYa7CTa2bKJgZWoYuBGmz5s3lggsuYAzFBQsWZE0optIxFT40Sf0cwDsm4mL/zDPPMujo/gfsz/EgYm4n1AZ5CaWY3w2Ma8EaxaKHmMsD+kgPCgLHH3/8MZXW6NGjadFcdNFF8sMPPzAR7QrML8U1P4208QO26EqEy7mbTjGU4po4AgZQ4uDpzjvv5EKWQ4cOZUMMfMVdHmvipSzuOd9nsfktjoIqNtflTt/tJtKuK861MRnD4oZw+/3nP/5Bq6Vesmv5en/O+7LpZptSIUAY4yOOvK2lgjONtNBygrUEYYlrKigQ0WLVqpXsFksm1LFCG0aRuaODCKQTBWUSXZBV0rlzF3bHwaPrK4wTQqBhfBDJrS0/eAYP2km/r736qlx+2WVy2O9/L82aNQ/ypvmLngN3fMQ4nDz88MNy+OGHc6Ip0gGe+MFigqca3M/hUHHCCScIlPD06dOpNIAByyMOpiwNzSeEP1zb4QaPzb0eY3J1IoV8YuXfbbfdlh6jsJxwTbHKEEFBxvANZAiW/5Fb/3HsnkfMXbiC0nIocM9P1y3HAumwLjS2d90StHlLOEqrSdMm8uc//0n+88IL8tTMmRQQ+JghKNAC51ZETFjHEiJzP5grrVq2FCzlrvVOu6qilIsKx7QgvBN+NZJKrSJJnGFLpWu4jhA80RYsmE+rpaYGQVNFPv/8U97feOOhfBd1Lc76xg456wrPcgFPibQMHDhAzjjjdJkw4XT5/vslGccM+juoM4FdlRfliXlTLCc4vOAgIXPmzJXzJl8gRx59jLRp0zZouZtCzQhpPS9kr/gSx1SKEUAw7tS7d2+Sg1WuygDKCRhjbhKuIaDrIYccwu5ARO4GLX22EF7W9g4cNuDR98knnwRWVDHTAz/Ik+7xXQEPNAY3GjpUDv/971HUrO8Ic0VZyzK0eimNHgTj7WnKVq9X8J71HHUddZ4+JWsr9jrfD1VQWskL3Vs5YwWHerv4fTieZmxHW20tWrSUyedNlltuuVWeeeYZttZ1XCqcRlz4mo8Yre6ttt46+JjjTJcKF56KCMrKca0EPfVSq6CsjBJu0qRaxuw2hh5VPy1bZgRLIiHvvDPLuKcP29iAZpVAnPy5tPDhQWiiC3bLX/xCfve7g2XChAmydOky8kyXfKuM8B42fR9lhu4j/N6b/Z6cedaZcuCBBwQrsRZLGKMeYYMHJpxMMPakvMG1W927f/75Z7qT6z28h243bRDpdRKL6Q9oK3+gP2LECFpyII/zYqSZy7qbBpxD1l23m/zxj38MlDEbKTrW6PCl/FXyHt+Dm/9sbFWbZ18t9CxUQaGlGuXnGgloj0Sh1djfZeER74ynGipA23ZtuQLvtddeK08//RQLRJ0FiomJaT6mGb15u1HbSZJeStHqg8svvPd0g5MD5tvAk2/p0h9tjD1YIWaRx2OPOZZeexiTAyYL5i+Qf933L5lw2mnSpnUbOh9QyHOQPT4eXX5BH1akbjvssKPss88+9LjE2A4/VmpZPGFsTU7mtERw/6OP5sv48afI7353iKzbrRu7DZWeCms9j7oHv0gTDYwXX3yRY0ywlBAxAlH0L7/8cjpH4Jmdd96Z86I+/fRTJgsngf/973/0sMPkVKUVlSf3feRXGyHoPoVChFs3jrGxPN0XYjxGnkEfPzQa4Ob+w/c/yIQJp1mHJBO5H8WI4jOtp2LVq/Kka8oow3uMxbMaqfBQR6Z0VnuhrhdgJqexFDJLmrWurq9W3HO5UAMzxH/Dx4TglFdffbVMOG0CPdowt4UfcO5LMaKGsvtp+XJ2+3Ts1JHdU3EKUeQLPwgIRIWA0ES7C9Yiulvg2l2NxQRTac7ZQdSIy6+4QvbZd1/p1LGTXPKXv8jIkdtwrChRVS3shiMekCjGgokRDpIygg1lAusuLbvuuguX+oYH3OWXXybt2rc3oals+uQCVkxNSubOmycnjx0nRxxxBGP9gSAENMpRhTXLNCamwesjjzwijE6SQLfiHFJGGvhBKcFBAhvi4qGb7bbbbuOEaMzFGjhwIKN3KE+6j4k9lj1ogS5wAC9QjPjpROW403R5V+WIxRNxDIXdtGkT0y6z5ULdZL+xIn5qLlvldUyAMiwDI5RZ3OUWrqAyafujUiOQFs4R4hcjafbRX3rpJYw/BwGOsD/YOK6hgg6tT+t5FzQK6so3uqUSSRORgV9jWubPny8DBg4wDcjYv1AzNwctZsS6ww8b5pNgjM2t5BDg6/XqJVdccQX7uG0PWvCMGSPSr6U4yom8AQPbFZmoruLw0pjdduNk1lNPPVUuuvhiuuPjWTMRmw/TCr3kkkvpoNC1a1cqJKPsDM/uMUGI4Q/w23PPPflTchDEwBL3cKwYoww233xz/vTZYu81bTcdxAn86KOPpF+/foEl5d6Pcqx5V6yxh0XZvVs3OeWUU6VZ0yZmWgUsZQbTNWUXJc1G/65+aqzGONFvMN6cZ/pacukizSg/25Ik2Sh0KvFdgIbyZpmzN1zat19Hpl45Ve6/735+XBTkBNcsqscBSnueN+bBCyhzM7CPdZ8223QztnYpUGIsB2bNtrZAmz+7bDaFqE5+1L3pyAsiPLjPQLEG7MfI42p1H4loeWBKALy8EgnZcccdOal1/LjxMn/+x7JqlVmrCv1DcHKZPPl83sfkYmwQlhCQpdyQHjDT9GtTEKXkJzct8IdoIYgJCIUZNz6gCWsdGGDM7R93/0PW69mTvRKYgAtBF9QpFrN3glit/rvflluAWpWtj4R7K47jcAW1Rg5dbms/Jt/KPDmt/bloWrAR09SsifDjwkeLtXSmTJ0ib7/1llz610vZJQKhifEO81G7gCuBuuzN4DTKggP+6ZS8O2uWDBo00InUUBc6dX3GafxoLUYFh6MBNipJW+PRHWj/6aPZz5gut6LXI6u4iRH5MZghoC1ck+Hdh6XAUTYoiwcffEgu++tlXDoD3WYQgHEL3iw81nDiKiT3eA2vlPwWJuzCanetuziZAP4YL7zppptkiy02F1i9jA5hq2JWnYso+4peFxsaf2zTmm8fdTzOeh7axWdFReF1JCBgDoLTwilWzpsEC90MJstwIEhj4DuVkpYtWsqks8+W66+7Xk4//XR6+rVq1VJW1aAVaF6AI0XegoiVzAhdjAV88cWX0qVLVy4kWN2kmp9EbAVQmwVh85rlLo5rTsXBmGZwnnNPsYqNR5dQwIMeGOUJnKsFLf6ErL/+BjJ16hQ568yzpHXbtvLT8p/kuOOOy4p7hzLJu1xcPhrpMTBp06YNrSdVUHHiBJoIX4RIGSiT3caMkZSNcVmF7lobc9LAC+vJd/GtqarhMww2GpvW1yC4GN9BqIKKo4JQ2LCJbwbQ4mO7kVOywjqTSwg2rAMBYYigqVVy/AknyCMPPyzHH3+c/Pncc6VP795W+GVezqcMUVaIDoji+vLLhTJw0EAKDIwLoUWEFmhsW4bFbJJ6Xfe46x7nnufey6YW35mmgw8zkF9oMBjU+L0mEtK0eXNp1baNvPe+CSmEwX/FDUJSrah8yiW+TDRcSqhfwAQxAOH+DsegfDZ9X9/RFjxo4vjtt9+Wx2fMkIsvupDRyROJtCTxY4MuLVBS2ZsWePZVf2YRcOHheDm6cfBtBK6PsUEVo9SJjcJQJcsAACAASURBVCdPKBeBoELAfIaeMhYSYqZNnDRJTp9wujz19DNcTwkfJASh+Ti1t8xt8uQSt1YKWvesYwmBy/GA/gOCKBZeoDqYsXENwYcGgxGAAA5x7rCWEibEnn322XSeQDQGjYKhYysqNB2KFX+omCDALeLyqYKpKzCo72gAYHPrP64hvBPc5m+97VYZNHCgHQM0lNEkMy2Ouqbknys1Al5BlRrxQtJT/WLdklWR4PsaMmR9ueGGG+SJxx9nkNkVK1dwzApOFJgEaxo1gYarPXXc1rGedJqz+odutJGZIoC/NN9qf7VirqIMbHcGu4SAF+Pqidx5513sbkUEBp3kigX5MCUAC//Nnj07EJwqQCsGtzpkFJigjsHLEfOh8t2giNAAcDdYYldeeSVX7r3++uukfbt2Ut3UWLT8fuzcPvbyrOXzcOn649Ii4BVUafEuLDUqEB2PwcdsBtzZKk/VyDod1mGcuH59+8oJxx/PjxxrSWG8prbhnlwmjP6zXylCHM2bK3379KZA1i6+3Hcq89xgpOMXi776mkukvPTSS1wMEAv/wVsMc3kgcIcMGcIxj+eee46TZDG2h01b+5WJ4eq5VgsKCgpjRfk2iPA8MMUPx1jfCo02zFE75uijpXmzZrxOf1h066HBhUrPYV7bZ7s6W/5KA0AgdAwq8KiKzKQZ2I6PXmSGGgEB0zkBpwl8bGiBwpFi//0PYCy1886bLNttN0p+s//+0rJVK0kgdpj1LqAwSOlsegsFB4WTxopKpeWbr7+Rlq1a21eMlquLomsEwDILHFmyuJrOdZMzzLnCv5pUSmY+9TQDqo4ZM4bjGngC5eBuUFbw4Dv66KPlySef5FyuAw44QHr27EmBqeNT+h7LxnbR6jWXXmM+Rt4xBqXx/zSvuJ67ARvt1tP72C9btkwefPBBYnvzzTdLu3Ztg1BUpgM7+AxIMgvjnLLLTdOfOwhkxAk7SWmF2kDSWZg6rxR6GKqgaqkXeaWRKW9TwaLSyyvxRv5wBlubUY6LYH2dpPTt10/QpXHjjTdRMP75T39iZAAIWopXO6ipH7ZaT3C+wDUMIGMMCp6BqGxsdVZY4cFChXJB3tPpGrra16wy82i++vprOf/88+Wn5T/TOoLrv2KZW+0MnqYBgegNWKDv9ttvlwEDBnBysjpRqMDV9+P+yJVuQ92zniUS9HhcvHgxLSFV3rXxrMoJ76nVBEcIRM+A+/ioUdtKE1ix0EdY5LLC6m9tmMV5jTLD+kWQLhvANoXV2xORkg5VUG7LsZAUIOiyBWnMnBfCVCN5J/O9mXahMZBM6x5ZxDLqGLDfcccd5IopU6R7t+4yfvw4Y00FDjfmIFMq/Jxl2bKfiFKT6iaBkwQvZBsHjQTJkGykRaqqqrmkB+IGUhCmU3LrLbfKIw8/Invsuaf0gxOJLQgVsHruUsU9CFQoPEzWPfHEEwULH06ZMoVjVMOHD2d4p9x3aqPlPtPYjpFfdFnDusR8pbZt2wZZVHz1As6x4Z3vv/9ebrnlFip/uJGb+IFGemEagDA0lanb+r7ZZ2p+9nV/tjYEWO1deRCEtGNzdm2v53U/XEFFLT9ITXWYB62o9PLKViU+DIBN1x1aBujyGzhokFx91VXy0EMPyx/+cJzsuecestdev5IWLVvYvg5bKNjZbj90sfTo0Z3lpYJB95WEKvIM5YTQUs89/5zcdONNAi+zE044XqqbNDWhoezgfi4urgCFEEUrX1v9sJq23HJLdgs+8MAD9DBDNyEEs+vpl0uzMZ8rRshjq1atZPny5YGCUizd/ANPRIR49NFHZdGiRXLWWWcxIjqeIdboCbDTIrDPrr+uZHWp+uO8EHDkOcW8a1HlRWjND4crqDW/5+82IARYVzJ/JGE9mtQDZu9f781lK6ZcMUX+cNwf5OijjuZYFQbzMeCPFpEKCQxSt2vXPsgdGqu4Z4ewzHWncgYPNqQDyqBwJhnwNfigjAKBEINSh0JKJKukJpWm9x0iyWPp+UMPPZTCkwLTWk7EpZZ8517Xc3cPCwE0sZotguX26NGDFpXOAVKhineYJpoUjuVQS7JlfwlKvHXr1pwLBYcJVezIt/6gmF579RX570svMajwb/b/TeCUQgByvPl4zZaXASi8XpQ9gI0wA+EKKnJDwzhHEDPQikyvEaJfoizB8May5aeeeoosXLhQ7rr7bpk+/Ro56eSTZMTw4XS0wORfRBpauHARW6/sPKSDE8ox56Mui7IMZ1I9EzU6hxYDuuFgOs6Z8wGjp6MlD1dxWDfYcB9CNI5NFQ+sMqzSO2/ePLn++uulW7dusvfee7MM3PTwvCq4ONKvTxpQNm5e9Bx7OJX89JPpZgbWuIY9lmSBN+R//vMf+e2BB3Asr3XrVhmxEl7c9ZnVxpk2xIGDNw7dIC9xZjpcQbkcFJBiZvxJc6L7Aoj5VyIhQOQpFJJci2jc2HGMe4aW+w3X3yC//vWvZcyYXdkS/e67b6Vz506C1WuxQB/nR7m1j5ZHjsKKxF2JXnbaS6zasEwQOR2TPNNmkcRXXn2FsdpgPW211dbWucR2G2GwvZAQUrVkT5WT3sI5HCcwwP/uu+8KPNBgSSHKO6J8Y4Oy0rk+KtD1/XLb15Z/5AH5gicfGgbYYEFBMWFJFiwLjwjtd999t7SHd56OLdnpFMFwQrmBUYb8qmwPpADbsPiTGQePK1uhCkqZiCuhuOnFxVcl0DFuoIhAYZZux3gglvk+44wz5Isvv2SMsnvu+Scjc6M7a9DgQZThuoJvqiZtF3MDWtp8CqpnmUBou4nIbYIxBnG4bMkSQeR2uCeje2/PPfaULut2pZMEBKa24F2l4B4XmnlXSKulgC7XjTbaSIYOHcrIFBDGiFGHZdgR7RvPQWiroio07YbwnuZfMQZPuAavSDg+IKIEFlvEHpOeJ02axPXJWB607E39Syaq2Zr38qWEpWpFAC0nJps5imjXrJaJUAWFbpBIG1uslnG0uqPSi8RMZb9sfP0yGOAj1wF5rIlz+oQJ8vOKFfLwQw/RIwrhejAmgommWMwOYzMqULA3Ex1plxlXbB3PYXHbiY8ct+IAVnZ/QIaNwo+c70GJqIDSZLP6IPgQ6jPi5xlr6aP5C+T+++9nKBwsh37Agb9lXqEEsAEjbMyvs3ev8YEIf5S2S1PTRRlAKaHB8O9//1seeughrtmE5dFhZbhbVtnYG6BT23X3vWIda9pKP/dcr2OvGEDxYnwJXdCPPfqoDBkyWA477DAZOXIk66pZ0RjdfUY6csViJRRRVCkZv88DAcVcJztTLMTfDR2qoPJg1T9axggYMSxcAhwr1n7++eey7KflcvMtt8ncuXMpFA8++GDp378/Bbw6kureKKuU7TUzEddhZJleQTOhOHZ4KKOUc+NEEIwrIXEoF8e5gDyKyKKFX8rf77hDnn32OencpQu96RARvmnTpmbek31HhWbsfNeBoKtUoCwRnQIhlNDthe4/rJKLuUJbb701V8NVharW1dp4X5OyqAN7dXpE81AbT1BEuK8/dF1ioUIsvQ7LCWNyyO8xRx9lLEU+i6pn5uSt3vCoE0v+oTJFwCuoMi24KGxTiEGGY0wFlm6VEeoaoqd79+6y9ciRXG/qnXfekUsuuYSz9DfYYAMZNWqUbL75CGnRrFmwciyC15qVcNkkNjRNQ7eoPYJUUZismU5JMmUUlTF8zDGE33vvvy8zn3xS3nzzTfl5xc/sQoPLPVztIazVklSBqQIc+/rYlA+krccQ6vBuw5wp/L766it566235LrrrqNihaULK1AXRdQ8KA33vNh5QlqaHvhWHnAMhYUfnCAwsRY/RH8A3xhvw2q66NL7/rtvgwjjtJhgDbJr2XKPotEWfLEz5OnXKwJeQdUr/PWUeJbstSfWFVeFCziDwho2bBgnQeJ8zpw59J668IILZPCggTJi8xEcL+nTpw+7ndDtAqHKVjKzxtHT+DNJAZXEKLpJC0vFp9KydNlS+fSTT6mUXnv1da7Qiu4wBHA96KCDpEnTJmyAJ7C+Vk64HPCNLeDfnsfPfN0pgkdsUKIYH4NwB3+dO3eWnXbaSUaPHk0B/8ILL9CywrNoXMDhAns8hzLEpuWK9/WYN2L8o/yCTz0G+e+++46KBxb5Z599RksJ3Zc6/wvPoDEB3tCljECvOKYlbMskUEhZdTdG5j2pBolAqIKKL3YeB6Myq6U2SBgqlCnXSqA8yMw3UUQgbKhwEgnBqqf44Ryz/dE1c82119MjsEOHDvR6wxjJoIGDZN2uXdlt2Lx5cyVFGUPdYoUPjl362YLT1hsKKDOMBWcPKEFEbF/+88+cpAmh9+qrr8oHH3zAKOy9e/cmH5tstqmM2n47dt8p/2TE5pMCUIVfwKE50Hs5l0t+qnwAF+CETTFCnrDBqQDLzkNhIRgtlAGsRSwxAWUAF3m4rsM6gdLC8+jSVHpuGjhWxaLp6LXcPdJ238U5xpDAA+bSffjhh0x/wYIFtP569epFKw+8tmzZcrV3mRnHlR/5w0Rp9B1TJ7l1FQ97RaWQlXzvGq8oBn6X+LpRRrnlFJG7UAUVtQGZ4VNbphE59a8XEYEEu8mQAMrd6I+MUMz1GoNww3wVxJbDD8IMXTWY1Y/lEmY+OVOW/vgjx02W/bRMuq3bjSFo2rZrK506dZauXbpIt+7dKIDatW8nzZo2o9JDHV+1cpX8sPgH7jEmgUFz/L77/juurfTJx5/QG7F1m9YUtHDmgACG5xsmv4IXt9sOeQK/KnCLCGLJSCMvqmBMmRnFgsYA3NIxyRUbrC5giHL58ssvGWIJbtsakBVda1AW+CFEEFzbcQw6sGQUN+yhfJYuXco9HDegCNFIQbmDHqwe0EBXJMbNUC7oEkbDBfQUf927YGkDAgoP3X+w/KCcVAFGlUVuWv44BgSglayW4i53nmQMSSiJUAUVcKBP5rn3sfjyBKyeH4cwwA9dZaqQzLkZ1K6NPX0HQgfu0BBOaKmnNs8MhEMgYtE+DOyjZT3vw3ky+73ZFHZ4D0JOBRTOIQwR7gY8oKWPFj/Oe/TsKRsOHSrtdm8nCBeEDc/jObUmVKCy9Z0zoRa8NpbNzQswwIa8K464j+vo3oPSwG/DDTfkc7gHxaXlAuWCH8oBigfXoYygeJSu7lHGeB9lgh+UIZQRFJuWGdLFT8sC7+Lc5ZmEnT+45z6Pczi9oMRM7hpP2TnZLt/D3OIIHFhK6cWXy0S+cPpYfPkiVm/PQ4CgQQLlBMHz3fffS8/1egUCL5ex2gSOCkf3Ho6hZCAg0ZKG8oLwcRWKKhN9T/cuPVd44b4KY91ToOnYV46wA++439g2xUnzppjqdWCj4zqKAe7hOW2AwNKCtQIaiqXihHN9HtfwDujhum64j0150LT1HHv8cF3vaTr6DN7HNaWNPSKR60Y11fiKT7NXnnsjLjK82/NifGaZmpBJzhyZupd7tc7nnBxKGrYTOSK9OifsHywQARRQWpo3byYLF31NGipcXGGCG+55rpBy7+FZva+CTQWV3tM09Fz3Sse9j3t67t7PfUefw76xbpp/zV/uOXBWzPGMloM+p0pKn3HLxX3eva/HYWkqbb3v0tF7uem4z0B5wnLr1Ws9kmCcSFhSXna4kDaM49wyscNPmaGdeNjMNIfioRdQybR8fPMnAKWBHqgLLxwQWrdpI199tSjgVAVLcMEfeASKgACUH+oauhq5Ai46+Cg6ciVhERL3JKMjYIsLVlScllSoBaXhcQrmPKhXOAC14ELBJP2LRUIAzR7UqnRaOnXsJD/9ZGKhFSk1T9YjkIWAWnfYYzysbdt2QTcwlJSJPu8bulmg1eNJlkWLYmEnmZHxWpZxsReqoKJWBzp2UCeBkrbR42Lb04kTAbfpgPGipUt/jJO8p+URWCMCsJx0zBEWFJdqx5QCY0Kx8RRVHq2RAX8zfwRKVCChCiqqncYIBapqqaNKlKP8oa74NyAg2PJJJqRT5050TQ6u2fELnPvNI1AsBLSLbzkXK2zHVnmiCioqYfpefPUrFvT5080tCz2HjIg55mq4gsqfbf9GmSJgBjZNF1+HdTrQJVxbtGWaJc92GSGg3UKoc5i3hXWeuKHrKHBhLqMMVRqr6IJRJeV2x8SAQ7iCipyQQwCHzmkMfHsSMSLAupVA5KA0wwEh+gDmymC+kQqPGJPzpDwCqyEACwou5pgMjAnXJiIBNZQRfl5+rIZZJVwomhefr0/lVH3SDEWVRFdfKs15S3D3hXLyXXvlVI7lyyvqGqwnzJXDZhpGxjXMN5IaerkWT9qHWlCRve4Cns1BZHoNvYzKnD/64NgyQ/BXRH7Q0EFlnjXPfgNHAI0gdO8hkoUJ05QTWYLjUIFAaeC5afzsocfFLQ1tQGCvx3GhEKqgtEux0ISyvfgyXZSF0vPvFQ8BVDY6RaSMxYRW7Luz3+PaPLiOrhdvSRUP/0qnDKGGLj7EDMSyIRrmCLgYOZQrEisdsfrPv+qHQHYoS3pDzyPu19DFh5QK/5HPLGYLpxWFD//u2nE3vlIm/hnqE+LeIRo1NggPr5yyv7J8W4n5Pp+dWuWcffrpp0ZB2RBJrHeIaM5t7fXYf+ulx8idCgDPb/0XV60NtaACr4xCU8qYUJl6Uygt/15xEbD2OipXKl0j6OLDongqWL2CysCvmGSurH6kzwA3j93q+OReUYwQyRyR6ekgAVnLesk1xXNf8ecNCQFbRCiyuDdtnsRN19MrJwS04QWJkEhIm9atpaZmFaNaQ3iowC2nLBWLVxWmoI9xE2xhGOE6vCHdd9BdCjw9ppkSgmNOzapVsuSHH6RVi2aqmXzDNgNRwzqyDdoMU8aOUjESp6IKt6AiRv3Txg+dI3ASkV4GDH8UNwIoHlQqLSJ48224wQZcBRULAGJ8wG9GEUEpQblA6eBYFwUEPqp0cA8L9WGZERyrQgKOWAIDq8m6SqvSsQUun3z8sfTv309SGI8yYFY6LA03/7kKiqGOTP3XbyAu5kMVlAqreBJCizEeSp5KcRBgG4LhZWgSyDbbbiv/+98r7O4rTorlRxUKCYoFXVFYsfa+++7jYnwXXXRRoLRwH6vKTp06lQreVWi4ByeAiRMnBtZX+aEQP8fA6J133pFNN92UCxUaIRdnOzx+niuZotuYLTYOoQoqagtPLScaf74vvtjlGAt9igS0+CUhm222mdxzz70yatSoQPjGkkgZE8E3AeGJPfB56qmnqKyQJbUyIWzfeustrjR84oknMrd4Hr8777xTNt988+BaGUMRK+vw2ps7b56ccsp448FnB9tjTcQTixUBt/mQbTW5d6InGaqgojpJJNIJhikJWIyX74CsP4gTAVtIaeEqqVjGGwJX1w6KM6VypQVFg+XQsRAjVpKFNYVrwAl7XcX2kEMOoXs+onFg3Amr1H7++ee0oNRtH89X4qYCDfnHb+WKFdK2TRvp1Kkj+5mx7EtU+VOJuNZXno0RYrrA467SfnChvkq1Qaeb5qqmGH/CWIrfMghAuMJagtJWq0mv4SkoH+CGDcpJFRfc9jEJFdHi9b0M1co6UsUE3PD76uuvpW/fPkLFRBcJPx7QoGtETvHknMbKeriCMoMSxtWzkGN3rnEh7/t3Csc+KnaYzZBMyo477iivv/56rBWuHIlBiOoWZvXoM1A+rgDGMZTUSy+9JNtvvz0FstKq9L1i89yzz8kvttqKcFChw3yKWof9+8XDECXl4uuex1ypwxVUxIQyn3REQv710iMAgZxOyw477BAM9JeeiYaTYm1KSVv/LpcqcHEPx6q0Vq5cKa+++qoMGTKE1hOsrErfFBsopDlz5sgWW2xpu/UwBuqlR3nVj+KVV+gYVORKEvBsDiLTK68SK29u0YBNpaRJdZX07NFdliAuX7t2gYNAbQK7vDMcnXvFRPcqgLGH0wQixHfo0IGKy4/pZeaOIbzR0I02lLbtWqPSSVWVaTN7eRG9ThaLgi7zR/pcpcfM1EWZab2PK+1QCwrDt1F+mUFOMxAchZZ/N1pZFIIfKhi6q7YbNYreaqh4EL64FncljKsyl5oO8KgNC8VKlRWsp+22285jl1NAwGnWrFkyZswYYoMxKHQtw4AqpM76d0qDW1bhUE8A+eJsoQoqalbJchbfvvpExbRU73PIBYtjJhOcD4U5KuiKwVabQC5O1Wy4VFUBYV+bwwMUk+KFOVHz5s2TESNGEDuPX/aEzjfffFOGDx9uxjSSFrdAeHiZUapvPlI6XBXFlBXqvjbM4viCQ7v4MhZQgcn4WHwFAlf/r6GqpVMiNakadkuN2HyELFy4UHr06EEhG2cFrP/c5s8BuugwjgTllBvKyKUGZYQJvYhtCNd0VWjYVzKGyDvwg9s9Yu/BXR/X0mnjqk8MqaRcNP1xg0EgGL7REDRmH7eLOfK7BgsqAhzMgJuLCLT8q/WAgGkFJZNVCM0nv9rrV/Lyyy9XtFB1CwHCFQIVzg+wlHCuSkf3eB7Hr7zyCq0ntahcOpV4DEywQcmjTmG+mG6YTwNcOa9GL5Zib3yCmBL4sz5CxqrDVbCsF3lsr2Xds4zqfXva6HcsTtua4HG8OQ61oLQiRUqODJvSj4VeJGb8y/kgwPJivUvIRhtvJH8+91xOSsUEVQiRSt4wOff555+XTz75hArqwQcflJEjR0rnzp2JDbADRujew2RnRJ2o5LE7xUPrDM5hecJBYsstt8yENwJuKvuLIOw0/dr2qhR1zwF/PMieIOPUoc6FgQOHwyP5Jv/wQrQKrbaEGsE110lCIcAe5YpfnFuogtLCKDixXBkWL98Fs+VfrBsCRgmZT7FF8xay++67c07UL37xi8BaqBulxvdUy5YtZfTo0bLrrrvSetIcAjMVxrCY0K03adKkQGnpc5W+B0aYF4awT8AMXcnVyaoMLBRyuQIkc7sYR1hmhsLVWnAqaHWM0RhQVm0x6D8chjBmZgSbuZM2UVc4Xlta/ouBSUOgGaqgjICKwmLaNj5QUPEOnEXhyr9bBwRQZBQSZtJpTU1KDjroIDnppJMECqqSrQGgB+GlGOA70Z8KNTyj91209ZvSvXuvMR8jvy42OMfY3A033EDsquC5pwPtui8hIGyGWUuJDXPwgF4CI7rY5WieQeHjnh17AY+ckoH6kBAsG4J8akSMEmah3pKiqAAMFrO463aogoqeY2U9OiVPocQIsFGI8jOKKpFIS4f2baVb1y7y4dwPpP+AAZJIVvFjNB+kfbbEbNZXcu5HqMcqgPUcvIUd1xff9ZUucNB6guOPPpwnm2y8kXTquI4d28GYnrWg6qmnBQFra1aukvkLFsjixUukZ48e7LKF5GXZWoWF46U/LpO5c+eZCcVsrCRk8OBB0rx5CwNxYxd9Ofljp2Y6ISkbACTOehauoKLKHLeigVZUenHm2tPKCwH0y6cTCTn8iMNl8nmT5bj+AyhYVCir8MmLqH+4YhBAdycsSuyhoDBm9+c//YnX1GIpqXxA7wAUD7vnIKgS8t1338n4U8Zzzl/Nqhpp06aNHHHkkXLyySczpiIWVEQ9RzDgq666SqZNu4rll0rVyKabbiKPPPII85eEoqU10ciL15XnsD6twRl3rsMVlKtgCkrVIYBD57Qgcv6lekOACiqdliGDh9BlGoPbXbp2JT8qeOqNOZ9wWSCgSgrBh+FWvuHQDdmLzO4y5KCE8gFJYaDfdNulqVguvPBC6dunrxxx2xGyZMliueyyy2XalVdKt3XXlQMP/G3QZYvpFgj8e9/999nuvoR06tTBWIhJdPeCNlMoi3IpiEkop6zyApjWOaQgguEvhSuobA7CKYTcyeKfz6x+JeRVf7mBIcCWryQkWZ2UfffdV/562WVy3PEnsDWsreIGxrJnpwEhoF2dqCszZ86U8ePG0XpJVllBzl3p5APlK5WIAQnWE7roDvv97wMX9xEjNmcsyieffJLjr1jpF9sDDzwgRx55pHHwoNmXFjhYII+wvBJNQB2KqnT5KXVRK3RqRBl9XBxv7VAFFQu8DhHnsNR4+vQiIoCPD79UOiWYtNu2bVtOsuzevXtW140KoojJ+dcbAQLa/ct6Y7v4Pv74Y66LhaC5GPOBTKAcL8LYxRohtMKITg2Spifmr3+9j1RXoXsuIamalHTq1JnLpsBjk3lJp2XJkh9l2rRp0r79OrLbbrvLPvvsIwMG9Gf8QHwbmNul30AlyDsoJlVSa8Q7ws3Qibro1onyjzw53Eeh5d+tXwTELiCXxAcoCTn11FPl0UcfDT5G/Sgj1EP/aiNDAHUit1489thjcsYZZ1Cg085g7L16qNvqeZlMSFWySrp07SIdOiKQrxGHJphvWr755hvZffc9mA9MWv/ss0/l1/vsywba9dddJ3vttZdMnTqVShdKDcqN+Y4kOesBj3z5RT7xz7jumW5NO/BWW7lHqdqhFlRU1cgVdbWbkLUxCpv+3fpEAMWH0Ee69e3bV1q3bi3vv/8+l5DwThKKjN8rAm6dgNCaPXs2Q2VtsMEG+ki2iHEas8EDRTogb6jT7JtCF12aiooDK2mcp+TRx2bIoEGDZJdddqEgxjPrb7CBnHP2JIGyQnzKiy/+i0yfPl169VpPfvOb33BMy9CE8C4S8w2FrJu/IjpJhFpQkXFgBtxcRKboCdQTAviOdUAZR4gmcdZZZ8mMGTPYPcKWVD3x5pNtmAgYQW14w9gTLO5jjz02WImYUcupJHLG20uQHdPyT7J7GtMlqqqqGdkCk27RNbd02TK5/bbbZNLZZ9Nrj1aBXYiyukkTQU/C0KEbybXXXiuDBw+Wa669RlbVGC8/Y1mUIBMNJQn2ZVJAqDkSK2fhCgoJR/6R+xjoxMGLp1FoeaKZkUR3jDY60mnp3m1d2XbbbeSFF15gS9QVSLHWUE+sLBGAUEedgHJ66cUXZeedRkufXr3o4caeIWs/oUqxuIbaXgAAGv9JREFUWkWWNXl+34KwSkyZ+KJbD1bSqpWr5KYbb6J7ef/+/ckcWCOfOidKUpJOr5LWbVrKKaeM54KLK1esNFMvtLRKnZ/6So+wYxpKccajQrv4TFtC0S5gD8C4mYPI9JSc35cegaAskXRaalKYLS9y5BFHyCGHHiqbbLIJu/wgkLw1VfriacgpLv5hsTz/3PNy1113BpqI84/qsw9MhbkDnPFGFbnttttoFSEMU7DZHoRASdlQRninV+9e0rtXL6mqxkRjO6mX3gMZ5RfQaSwHwM/JHntKIRmKEIsv3IJqLGD6fMSDgFbIRIKD3OiHb9G8uYwdO1b++c9/Bmngo/VbZSMAQaWhnv7970dk7Lix0qZtW67SDMGG+/W62boMPhAHEHUWS33cdutt0qx5M9nVLqCIPCxauFDmz/9IUjU17M5GkFuNXp9MJOTdWbPkuOOOowcguwL1O6nXDDaexEMtKNf8LSi7QUU0JRaZXkFM+JdiQUA/OprxcA82AgYf8MittpL77ruPK6NiAJxdJTZiQCxpeyJlhwAENQQ5HCMwXrnD9jtIOl0jVdXVnJyLxk29b6zTaYEzV03NKrnrrrvk1ltvld12GyMXX3RRwB66sG+44UZ66E254gpp2rSZ7H/A/rLOOu3ljdffknfemSWnnnYqv4jgM7HegAGRxnagGdV84RyyoRbPTX2k0H2ogiqUYNZ7uRnJuulPyhWBTLGaLr2JZ02UI486ilEm2rVrxxZpuebN810YAhBOsCzQaMGGpUYwKfeaa66RanZ/mYmcCKpa3xsbWHa+E5pazzz7rFx++RX03rv11ts4R8u2wbgcCJZRwdajZ0+ZMmWK3HPPP2XUqG1lt913l9PPON2Oz5pBGOCg79Z3PkuXPhAtdSSJqPXIteJBKyq90qHtU1orAgmRFJYWqJaqapEuXTpzdv3//d//yaGHHrrWt/0DjQ8BdJOp9QxFdccdd8jhhx8uHTt0pMA3PSgQCkUaTc8HUjvBFJYcJgyP3mm0vPHmGwEFM4SEWH0pgbchlA7yd+CBB8qBBxzILKB7kM4eNqYfFZPaUY04ikQAknuQNqVbDBEfPgaFuhTl5zYjotDx70Yrh6Lg50wht4d77LGHdOnSRV577TW36vrjCkJAxx8xR6h3794yZswYSYsdk2QjFX+MJRVJtkSs0xSnoGHZMY1nY/lA0WDCLhVQMkk2kS9cD3wfbARzEOB4mjp80HoyLtf1mb+Sp207/QFp3NsauviiJbf626tfiTsznl7pEOCHyS/BtJvQdTNhwgQ56qijpFevXmapgtKx41OqZwSMAE/LV199JU8//bTcdNNNFN5mnSSNsgAmIQdUM9QP05REVhzpeCoUKRQTIkIYJWXqtQn8Shc1Y0lZT1VVxlB2iLtHhSZWsZlX6ydzJU41kOrQ3kXw4gtXUNoqKCTDbg3A+yiwKPQK4cG/U1QE8BHrxo8zlZZ2bVrLheefJ6eeNkFOHjuOkxzVm8t9Xt/z+/JEgOVt5wThGF172K9cuVLuvvtuufCC86XDOu1s5lBP3OkHmXpTX7knBzlsmE4qkURVTqeSU8/Br9ZjDYukechczyGsDzSmPeS7zSZ2Wh+AgeIQV3ZzSiMusgH/8RH0lBouAqiYdqmBQYMGc+wBggqVVStvw2Xec5YvAlqueA8NEIw5YcO4E0L+DBw4iOe0LijLKkBoM8eV+qd45VscBUV+i8d0pVaDBptvWvemWYUuk1/utRc9+rBUAba4W1UNFocKYkzLFHv8EPZq8KBB8pv99pWqKquaYH3wV0HAVEJWSyjai6OgKqGQfB4DBCCD0JLGbHp091Qlk4x4/vnnn8u7774btLCDF/xBWSOg4y/IBI4RNPjzzz6TsWNPZj0w3V/WGYJjTmWdXc/82hBwFRaO3fO1vbuW++FjUMHo11oohN52CODQOQ19xd8oWwTYh289+jArv2mTarnwggvk+BNOEMyN6tmzZ5A33+0XQFGWB7CYUIZolMyfP18ef3yGXHvNNdK8efPgQ8fnTjnlv/uyLOP8mMaHb+dBxVzeoQoKFTDShtpJEvhjvFwi0fMvlw0CWGNnVU2NdOrUUS7761/llFNPlf3220+6devGPGj3UNlkyDNKhQQYtHGBMvziiy/k4Ycekkv+8hfpsM46DBekzgZ81rdKK6LmGE1RHC++8C4+NdUK3ecWTaF0/HumKdrAcdDhBjSbMbkRXX1oYfdabz0555yz5c4775QffviBAi5y4ye3bvnzoiKQW144X7x4sdx889/kzDPP4LQCbXTAWYabDj818HpLM8/zmJ+MQQG7mBWx9oVaUFrhCkrbWk4Iwc6cFMH9sCC+/EvFQQDlzbI2OwgwKCdYzjXplGy4wYZy9tlnyznnnCMnnniitGjRwo5V2JeKw5WnGhMCubIAygkhjM479zwZNmwYi56L/qmLNpVTpmwzRzEx5MnUPwK5hWrLPLeuRGU03IKKQpnM5+YgCkH/boNGIKeoUUlhUWGDwwS8uoZvtqlMPOsMueH6a2Xp0h9pSbmD7Q06fxXKnAob7NWKghV80403yJ/OniQjhm9mnPQSCXEMJ++12djrS873XkwHg1ALKnr3semZZFnh0Dlt7OXn82cQgDdXosqMP0JJbb31SKlZVSNXTpsmB//uEEabQNRrneipAhHCUI89lvWDAMpAlRIaErCIESUCUb/HjRvHIKpUXPiwqaCqAivaf+v1U2b1mWqxRHy4gopYy6iPspRS1kl9YunTLhUCthIELfB0WrbZZhvp0LGjTDr7HDnkkEOka9euq0U/98qpVAVUezpuA0GPoZyuuWa6XHThhTJ8+PDAAsbUAjao7fI6OEaxr9bIrj0pf7XMEQikuoY6iqg3cuEIVVBBwrlv1PU8IGAOgtO6vu+fK3sEuHIUnXtMwNBkVVJSqbRsuOFQueSSS2T8+PGMEI3AorqpQNRzv68fBBAdQhsKcCW/95575MqpU7naLKwpRPo2q8gKF/2D5yZjsdm+Xf+910+5lSJVbYRoWrS0tU8/5oIPVVBaOZWJvPYQSkHIeYye+WgCeeHXiB6md5/Tnra+EzJowAC2yCdOnMSBdiyxjYpO4ee7+OqlBgB/ChuMHVZV0bJ944035L8vvSTXTJ8uPXp0p9JCmSa5xpNhE89iy41PVy+Z8IkWHwHTq5udjnWEi6Q3sinyrDhOEt7ErwVqf0kRUJu6Z48ectVV0xiJAKFysEFAxl3JNV2/rx0BVUrAXRUTLKjHH39c3nnnbbn22muk53o9Tb9dsFJ27bT81UpEoHgdusVRUOS3eExXYhVoTHmmVZVM0lpq26YNW+ft27eXW265RZYvXx5k1W3RBxf9QdEQAN5wiIDjCsoCk2+vmjZN2rZtyzTRjcfGQ8zdOEXLkCdcHARKKNqLo6CKA4un2kgQcFvsnNRbXSUnn3yyHHDAATJt2jT59NNPg+4+ZFmfbyTZb5DZUJf/L7/8UqZOnSoHHXSQnDz25GDOGpdqt131Zo5bg8yGZ6o+EHAVFo7d84j8hI5BRXXG4EJgbkvLPY7ItH+9/BEwY1PUPmbAPZmQXXbeSfr37SPnX3CBDB6yvowcOZLKqbq6mi173/UXX7mr0tcxPzg4vPCfF+SDDz6Qyy69VPoP6CdNMLbEZWQhc3Kkjv+e4yuMcqdk6wjril1AOa4shSoorcBREzKKKjP4GpWef7+RIEB5BymHMSeRajsoP2jQILnuuuvkkkv/ylVZsb4Qgs1iQysfSsorqsLqAL5p/BQ/7IHp999/L/fee68MHDBArp5+tbRA0FesEmtbqfB38vqoMMwb41v4dMPrQ/idQrAIVVAQGlE2shnwmoksEIWmf7dxIIBqYVrkxh0IghKNMLTmUzU10qxZM5k4caK8/PLLct5558no0aM5MRS5166oxoFE/eQCSgpYwxHi1VdflWefeUYmnDZBttp6K0licjUXnzRlwgYErafgY64fpn2qDQeBHC8+fLvF2kIVVBCrpsCU2epKpI0ggrKLqvEK5MO/1vAQ4AwENoASaKizNWaqB1r4IpgvlUinqZSwSivivl199dUco+rQoUPDy1CZcORaThhr+te//iXrDxkiN998s6yzTgd256EBUFVVbcb9tOvGllWZZNOzWQoEcgwYfL+oX1rH4mIhXEHFlYKn4xHIRQCV22l1BW2XdEIw3mS6lhJSJWnp2GEdmTTxLHn55f/J1dOnS/fu3WXHHXeUJk2aZH0MxgozloF2BeYmW2nnsJSAhY4zYf/zzz/LzJkz5fPPP5Pjjz9Othk5UpJB7EQUTJL4s0yCgqk05Hx+14qAfr9UVDjJ0VhrJVC3B8IVlDJQNzq1POUQwKFzWsvD/lKlIcD6rJXaVg6covsA/3BsBSSE7GabbcogpXfedRc9/XbeeWcZOnRoMG9HW28QypW+KQbAROMcAsO3335bHnvsMdl3333k/MnnCtzGFS22fIG34qc3Kh1Mn/81I6D1hBFj1vxoIXfDFVRQdQsha/WRMk8SWSeFEfVvNRoEjBxEFzA2VVQ4Xr2eQG5WV1dRdv7u4INl9913l7///Q6ZMmWK7LXXXjJgwABDJZHguIoKZV6swD86vgSlhA2eeQ888IBst9128re//Y1WKawmukGk0pKuShrnCWCv8LtFUoEY+izngQCqDfvt43eGC1VQWk/zYDP70YCAOQhOs5/yZ5WIAFtb1qMMA/KrYWCaY7AEUG/4hO2GwnGnjp24rtQ+++wj1157rTz66KOy0047yZAhQ2gxuHHkaBmsRr/xXtBuPeTwvffeE0ToWH/99anM+/Xrx+4+aqF0irgmq5NBazINfcbCWL1EGi9iPmf5IkBdpC/B6IYnbi1fsT4SZR+qoOL4sFW8gPc46EXJqH+34SDAekETKiHpGgR+Yy1nj15aUqZrLy2SEjOmhLpjlJTmwQzG9lqvh1ww+VxZsOBjufHGG+TpmU8yWvrgIUOkabPmtAogsGFRlPOGPAAD7LG5x3oOawnXV6xYIe/Oekf+8/zzAoU05fLLuOKteU7suk0Ipmfi55Gg/+MRyAcBt/0CpyZ0ceAa9+7NfIjW/myogqr9cX/VIxAdAQjSVTUpWbhwEZeHZwVnDU9LAg16GFB2cH+dDuvQcYLRsoOkTddgDYSyJKRXr/U4uRdLQtx5xx1y+eVXyPARI2SLLbYI5lAFr5bhARSsKiCwr0rXVVxY5faFF16QN998U8aM2ZVejx07dQzc8oG52bQvQ8/LEBDPcsUg4BVUxRR1w8koBGtNzSr54osv5JZbbpX7779fttrqF7LJJsMsk2l5993ZgkjaMx6fQc+9LO4pY40DAK+nk4Ilxzt36SJjx42XI448Sp57/j9y3333yTfffCPbb7+9bLTRRrSk1PrICGwj8N3zrLQawAmUkyopjK+hCxMYrly5UmbPni1PPPGEdOzYUfbbbz8588wzpXWrVlKFJW5tzwXehSKn5QpFpTqqAeTNs+ARWBMCXkGtCR1/r2gINGnaTDbdbFOusAsFhbBGf/zjCcYrL52iBXXueefJqpWrjEB1G/x6bBUVrK4kjvFLiLRu00Z22WUXGTNmjMydO1cefPBBRqVo2rQpF9tDtIrmzZtnWSVFy2gMhKE8oZSgaBBMF0rp9ddfp4IaNmyYXHzxxYI8YaN1xR486/iglhMwsxgVc8wghux6Eh6BAIFQBZVO8esPHiz8AP016LKJi17hnPg3GxACGJFPs4kv6XRKampSktR1haBnklVyzDHHSMuWrcg0BG/tLX8zudf0geNR0/1XbT3TBvTvJ+PHjeX4zJw5c+T222+XGTMeky5dutJNvWfPntKpUycK9tqsK0UM6et9XFOLS6/rc+6ePNtn9bncvT6v1/UcA9Epei0IrcBPPvlEZr0zi1bnJptuwjzB+QF8cHxOYJXWUMHTSML3ZocGCJ0dvzLjwkaRaVp+7xHICwFt7Jj2oLHMYaE764nlRW8ND4cqKG14reHdNd6y34PNghk/W+ML/mZFIQBrIJ1OCKNki9mzEYMYcGmR+fM/lL594XWGrqk11x/WNaf9Y98wSgQV2U7vGTJ4sJw/ebKsXLVKPvn0M/nvf//L7jEorj59+tALEEIf1hUmDGNzlRLOVZFg73a9UVE4Hw3u6/s8sO8qDX3XpQca6Lb7cclimfvBXHl39ruyYMECGTJ4CC3MX008U7qtu640bdaM1pRJg+hQPyctz6qE1NB02FJW/N4jUDACrNm28UMiaGjq5hzqpSj7UAXFrzoC5YQVNBkSMXOeIeyPyhABCGNu6J+D8E7BQQJKq0aWLVsqjz02Q44/4QRjBTjKx7yU/Zek3OpFy8w+A8MrCJBqrKCmzZpKvz69pV+/vvLbA/aXpUuXyty582T27Hflvy++IF8uXCQLFy2SLl268Icl6RHBok2bNlRYOh7EsR2bjyA/Ntncc30Ht8EPxpIQpBXjcFhS/dtvv+UyI127dpVu63aVYRtvLKNH7yQDBg6UVi1bkmpNqkaqq5vwGEoYaRh70br5AgM70dmy4XcegdgRYJV3v8kgpJ1a8/ElGa6g3A++kPQoJGwuQCsqvUJ48O80SASoMIIKYeZDzXzqKfnyyy9YT2bNmiWbbbaZcTtXU1wVWl1z5LxHQQ6PPyrANMe3zLUaCvlWrVrJsGEb84fuxkSiSn5ctkw++ugjRl/A+lTg6euvvw7WR0LIIIRbatGiBRUXjo1FYxhUpQiLaNmyZfLjjz/SBRzWGRYEhDs4lVG3brLhhhty2Xu4hbds2ZKu4OlUjekatwoNno4I5JquqWEw1zS79ox6Mh8XvjXVUP5jq2s18c8ViIBTxTgvyrWoCiRZ22vhCqq2p/01j0AMCNC6CNoupu961KhRcuKJfxTMg3r7rbdk5synzJgTFJMqm7qmzY/H+YIguu1cKKRtxmzQfWfmAmXrPmPRtW3dSoZtNJQ/Jgs2UmacJ5Wq4ZjZkh+XCNy7F//wg6xYsZL6waRq5ywlRJpUN+GKtG3btaXLO5QMrCfyQe86ZNNYQ0H2YAXVMk8pa+ZSdvYyLcDszAQk/YFHoBwRCFdQrglXUM6cQW3QikyvICb8Sw0ZASoLs8wGLBBYF6gomL+0ePESM/jKebv16xrNMR0qjYRUJaqkKp2U6iYJQVchHCzYrQbFYJWGWk9GsSYEXXNBdyAVrh1Tc5R03t+H/54acs1u3Lyhnjv1D4ewopxLseU/XEFFTC7T6FW2dR8b755QGSOA+gFBzn/YM24cHA/Q7ZZkxHIzLmWskTgNg0JqIq0uvAjvOttdCD7RJciNGcqYNVRScPDQSBb0cDJfsulezBRebt7qwl8mpQwdf+QRKAUCKtuDOohvmRrKfM9x8hCqoJSJuBKLm15cfHk69YEAFFGak2uxh9THRFscU3ijy8sumodr9OSri9TOJyvB11WHl9g6NG7bsJLoDm/5Ydeh8maNKJ5SYRkvQCg141FvLUHcU61ERZ3poasDN1SSmmSdnvcPeQTiRADfDr8J7TRAbbQfVMwVM1RBQUBE2vSjBuP4H5VeJGb8yw0LASxUWCOJdEKWL/+JC+TBmQDKCRt2OEKdqcIRBHp91p/aPgX3mnusn6oqIGYI+bEPcee84BzWuYwKeafOxP2DHoE6IKB1kO02K+PRZe/W+zqQWdsjoQpqbS/6+x6BQhFAt9dPy5fL3266Wf7f/3uUXWaPPPKING1aLQcffBBdu01QPk1BvwY993uPgEegEhDwCqoSSrkB5hHu2Zjn9McTTzLu2ZirBCsJ4c3V087rpQZYcp4lj0DpECjvdQhKh5NPKUYEtBuAnm22S8+MyWCQ1dFKdhwnor9OjJx7Uh4Bj0ApEQi1oBh2JhZOzGhafPRiYcoTqWcEjFccVnwyG9WS9UMwA7B6x+71tJ759sl7BCodAacJye/XNCvtWDEalTFuoQoq6lhXhk+Tnaj0YsyzJ+UR8Ah4BDwChSIAHWS1lGlYuiqrUKK1vxeqoAIOan9vrVd9LL61QuQf8Ah4BDwC5YdArj7SWHzwVY3ZEglXULlM5Aujj8WXL2L+eY+AR8Aj0PARcCwoMmvPY9ZNJB2uoCJ2JaJf0gww2H1Eeg2/1DyHHgGPgEegQhDIlecQ8/YXJwJF8+LjIDitsKimWJzZ9bQ8Ah4Bj4BHIHYEdHI99jGK/FALihZQlFwEGhYHoBZciELVv+sR8Ah4BDwC9YgAl9fQ9KGM2ElmZDwm4ce5hSqoqEoQQ1BGJ+EgCPQSJ++elkfAI+AR8AjUBwJRFUQdeQ5VUFHtNAa3VVVLHVWiHNUx4/4xj4BHwCPgESgAgVxRrufo24s5ZmbRxqAKyLZ/xSPgEfAIeATKDQG3V8+M6MSWg3ALyk20oOQcAjEzXRA7/iWPgEfAI+ARKCsEimZBOeqprADxzHoEPAIeAY9APggUT9qHWlCRve5yeF7Nu0P7LfPBwT/rEfAIeAQ8AvWKAES3K95VtmOvx3ExGKqgouqPjBefYdX4xitVN3txZcXT8Qh4BDwCHoFSIOBKcoQ3CiS63oiJiVAFFTkWH7QsvfiUdTuTC4xTe8WUA0/GI+AR8Ah4BOoFAegj9rbBAtF13GLkJFxBRdWEqpfIrD3BDnSj0o4RAE/KI+AR8Ah4BCIgYJfJKYZYD1dQWQomP+ahUWH21ayqkVRKRJJVklKtBLq67k9+ZP3THgGPgEfAI9DAEEDwCBpQ6YQkpSpW7ormxRcrl56YR8Aj4BHwCFQcAol03G4XFQehz7BHwCPgEfAIFAMBb0EVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI+AVVGQIPQGPgEfAI+ARKAYCXkEVA1VP0yPgEfAIeAQiI/D/AUWsOZSSm17SAAAAAElFTkSuQmCC" alt></p>
<p><em><strong>(A1)</strong></em></p>
<p> </p>
<p>ii) \(20 + 28 + 17\) <em><strong>(M1)</strong></em></p>
<p><strong>OR</strong></p>
<p>\((100 + 95 - 68) - (10 + 40 + 12)\) <em><strong>(M1)</strong></em></p>
<p>\( = 65\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note: </strong>Award<strong><em> (M1)</em> </strong>for addition of the correct values from their diagram. Follow through from part (a) or (b) and part (c)(i).</p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i) \(\frac{{100}}{{160}}\,\,\left( {\frac{5}{8},\,\,0.625,\,\,62.5\% } \right)\) <em><strong>(A1)(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em> for correct numerator, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct denominator. Follow through from part (b).</p>
<p> </p>
<p>ii) \(\frac{{20}}{{65}}\,\,\left( {\frac{4}{{13}},\,\,0.308,\,\,30.8\% } \right)\,\,\,(0.307692...)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct numerator, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct denominator. Follow through from part (a).</p>
<p> </p>
<p>iii) \(\frac{{90}}{{160}}\,\,\left( {\frac{9}{{16}},\,\,0.563,\,\,56.3\% } \right)\,\,\,(0.5625)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(A1)</strong></em><strong>(ft)</strong></p>
<p><strong>Note:</strong> Award <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct numerator, <em><strong>(A1)</strong></em><strong>(ft)</strong> for correct denominator. Follow through from parts (a) and (b).</p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{{100}}{{160}} \times 850\) <em><strong>(M1)</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>(M1)</strong></em> for their part (d)(i) multiplied by \(850\).</p>
<p>\( = 531\,\,\,(531.25)\) <em><strong>(A1)</strong></em><strong>(ft)</strong><em><strong>(G2)</strong></em></p>
<p><strong>Note: </strong>Follow through from part (d)(i) or from part (b).</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Venn diagram, probability and expected value.<br>Candidates were able to draw a labelled Venn diagram and correctly place 40 and 25. A common mistake was to misinterpret the intersection of sets. In most cases this resulted only in the loss of 2 marks. Many added correctly the values in their diagram and follow-through marks were awarded irrespective of working seen, allowing the candidates who produced an incorrect diagram to obtain full marks further in the question. The most common error was not including the 25 in their total. For part (c) many correct areas, but also many incorrect areas were seen. Again follow-through marks were awarded for part (c)(ii) irrespective of working shown. Some candidates just counted the number of regions. The simple probabilities in (d)(i) and (iii) were answered correctly by the majority, the conditional probability in part (d)(ii) had very often an incorrect denominator. Some candidates with an incorrect Venn diagram lost a mark in part (d)(i) as they used the value from their diagram for the numerator and not the 100 given in the question. Candidates should be aware that when values are given in the question those should always be used and follow-through marks will not be available. Many were able to find the expected number of students in part (e). Some candidates lost follow-through marks for not showing their working here.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Venn diagram, probability and expected value.</p>
<p>Candidates were able to draw a labelled Venn diagram and correctly place 40 and 25. A common mistake was to misinterpret the intersection of sets. In most cases this resulted only in the loss of 2 marks. Many added correctly the values in their diagram and follow-through marks were awarded irrespective of working seen, allowing the candidates who produced an incorrect diagram to obtain full marks further in the question. The most common error was not including the 25 in their total. For part (c) many correct areas, but also many incorrect areas were seen. Again follow-through marks were awarded for part (c)(ii) irrespective of working shown. Some candidates just counted the number of regions. The simple probabilities in (d)(i) and (iii) were answered correctly by the majority, the conditional probability in part (d)(ii) had very often an incorrect denominator. Some candidates with an incorrect Venn diagram lost a mark in part (d)(i) as they used the value from their diagram for the numerator and not the 100 given in the question. Candidates should be aware that when values are given in the question those should always be used and follow-through marks will not be available. Many were able to find the expected number of students in part (e). Some candidates lost follow-through marks for not showing their working here.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Question 2: Venn diagram, probability and expected value.</p>
<p>Candidates were able to draw a labelled Venn diagram and correctly place 40 and 25. A common mistake was to misinterpret the intersection of sets. In most cases this resulted only in the loss of 2 marks. Many added correctly the values in their diagram and follow-through marks were awarded irrespective of working seen, allowing the candidates who produced an incorrect diagram to obtain full marks further in the question. The most common error was not including the 25 in their total. For part (c) many correct areas, but also many incorrect areas were seen. Again follow-through marks were awarded for part (c)(ii) irrespective of working shown. Some candidates just counted the number of regions. The simple probabilities in (d)(i) and (iii) were answered correctly by the majority, the conditional probability in part (d)(ii) had very often an incorrect denominator. Some candidates with an incorrect Venn diagram lost a mark in part (d)(i) as they used the value from their diagram for the numerator and not the 100 given in the question. Candidates should be aware that when values are given in the question those should always be used and follow-through marks will not be available. Many were able to find the expected number of students in part (e). Some candidates lost follow-through marks for not showing their working here.</p>
<div class="question_part_label">c.</div>
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<div class="question" style="padding-left: 20px;">
<p>Question 2: Venn diagram, probability and expected value.</p>
<p>Candidates were able to draw a labelled Venn diagram and correctly place 40 and 25. A common mistake was to misinterpret the intersection of sets. In most cases this resulted only in the loss of 2 marks. Many added correctly the values in their diagram and follow-through marks were awarded irrespective of working seen, allowing the candidates who produced an incorrect diagram to obtain full marks further in the question. The most common error was not including the 25 in their total. For part (c) many correct areas, but also many incorrect areas were seen. Again follow-through marks were awarded for part (c)(ii) irrespective of working shown. Some candidates just counted the number of regions. The simple probabilities in (d)(i) and (iii) were answered correctly by the majority, the conditional probability in part (d)(ii) had very often an incorrect denominator. Some candidates with an incorrect Venn diagram lost a mark in part (d)(i) as they used the value from their diagram for the numerator and not the 100 given in the question. Candidates should be aware that when values are given in the question those should always be used and follow-through marks will not be available. Many were able to find the expected number of students in part (e). Some candidates lost follow-through marks for not showing their working here.</p>
<div class="question_part_label">d.</div>
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<div class="question" style="padding-left: 20px;">
<p>Question 2: Venn diagram, probability and expected value.</p>
<p>Candidates were able to draw a labelled Venn diagram and correctly place 40 and 25. A common mistake was to misinterpret the intersection of sets. In most cases this resulted only in the loss of 2 marks. Many added correctly the values in their diagram and follow-through marks were awarded irrespective of working seen, allowing the candidates who produced an incorrect diagram to obtain full marks further in the question. The most common error was not including the 25 in their total. For part (c) many correct areas, but also many incorrect areas were seen. Again follow-through marks were awarded for part (c)(ii) irrespective of working shown. Some candidates just counted the number of regions. The simple probabilities in (d)(i) and (iii) were answered correctly by the majority, the conditional probability in part (d)(ii) had very often an incorrect denominator. Some candidates with an incorrect Venn diagram lost a mark in part (d)(i) as they used the value from their diagram for the numerator and not the 100 given in the question. Candidates should be aware that when values are given in the question those should always be used and follow-through marks will not be available. Many were able to find the expected number of students in part (e). Some candidates lost follow-through marks for not showing their working here.</p>
<div class="question_part_label">e.</div>
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