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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>
<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>
<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>
<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>
<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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SRAOwnQTgJCWhJQfkiAdhKgnQRoJwEhLQkoPyRAOwnQTgK0k4CQlgSUHxKgnQRoJwHaSUBISwLKDwnQTgK0kwDtJCCkJQHlhwRoJwHaSYB2EhDSkoDyQwK0kwDtJEA7CQhpSUD5IQHaSYB2EqCdBIS0JKD8kADtJEA7CdBOAkJaElB+SIB2EqCdBGgnASEtCSg/JEA7CdBOArSTgJCWBJQfEqCdBGgnAdpJQEhLAsoPCdBOArSTAO0kIKQlAeWHBGgnAdpJgHYSENKSgPJDArSTAO0kQDsJCGlJQPkhAdpJgHYSoJ0EhLQkoPyQAO0kQDsJ0E4CQloSUH5IgHYSoJ0EaCcBIS0JKD8kQDsJ0E4CtJOAkJYElB8SoJ0EaCcB2klASEsCyg8J0E4CtJMA7SQgpCUB5YcEaCcB2kmAdhIQ0pKA8kMCtJMA7SRAOwnrD2lVyWDDhg0bNmzY1rWtOaRXeTu4GtBOArSTAO0kQDsJM7UjpMUD2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CQhpSYB2EqCdBGgnAdpJQEhLArSTAO0kQDsJ0E4CQloSoJ0EaCcB2kmAdhIQ0pIA7SRAOwnQTgK0k4CQlgRoJwHaSYB2EqCdBIS0JEA7CdBOArSTAO0kIKQlAdpJgHYSoJ0EaCcBIS0J0E4CtJMA7SRAOwkIaUmAdhKgnQRoJwHaSUBIR2Gu1f+5ufeNZjj+L056ta1Sc+Be8Jbad/qQXdNOzkZk7QID7SRAOwnQToKAIc2GnXJuzqNCturG6dU/2THq2YyqZPLLh7T/ltw2QvoqnBraVnDsYg6ZPTjQyqqSyVeeHttjyn1ciGjamWM08slSs9uxzoPXbfO5VlIyanavPbBpT+kFiKadc+5YR+1qNqMqGTW71zqyYlUKtK+Ca71r7uWVjKrkStoLM15dLKpJRNae7pDmnHPOLH07GcnOUP/X/VVCmvtXAJOQXvYttxHSV4CNuvvZWVHhDlrFnfvGiPGxbTwsFdumm9ISJJr26FVRsJV1y7d7Zja/LzWObMaZfXS/+H3LPKPd3XmIpn086t7LZ2udocO55/ZOpO6C9hVgJ68f//jO8sS+b1cKarS6WFSTiK1d0JDm3Pmt10dIi8KZ2dyb1fNxbum7kUNwamh3yPXOQzDtTr/176NIk4E5xoNwpIZZ+na2YTgseKmRn+R3uhBMe7JWiZ3h0L4K7Mv7/mjSPo7nwqKaRHTtQoY0s96+DptiV/9chPR14Y0UFLVOt29FG8pJn+KVn9TC7C9fkqrvBh0Y55a+q0Y9O0Y9G+neSBNiafc7MCbNuFND24kGCbSvDceoZ4NcWFSTCK9dxJAej7rtg0l/qWW8alZ3dMsZ9vwBiYPhpHoKx4dyJa07lRBhSE/NI3O9TytUm93j/m8fvasw/1T47FjdejGnKoWq/mn+RLNNIUD5iXFu6buTHtdio2cF0wCSR9YbRhWp/IgCs/Tvat2R35aYujx1jHqWfrLFTETTzlyzXfJroXPbaNYfv7ehfRM4Rv3Wvd5ozBfXJOJrFyWk581/CQbeij+0nv9ms8QBYI7RyBcfGvaYc2eo17x5NP4Bix685Dyyc0uv7XdPGOecj0eHL/uRkC7VHh0MbOYNPlEkigDlZwZj2/ylo5VVJRO0M6YjGSG9Ic4t/YdJFTZdSYlWbaWbsT14Wp2eZArt64Q5xoNtf57vwppEfO2ihHT0KskZ6o8mLWkvp8PejNh106mhbU2uoRyjnt2ZTBlIXGFFf2TDTnmr2uyaySmCsU6V2YPlmyf15WcBY9t4WPKlIaSvCzbs7DwIxuSQFpuGudZhq/moXsypSvm+4fdfQPs6cQetypNgTAEhfclPXDsXjUlfKqQjx2ZBSPut5Iya3Wu9igyjIqTXwOSgoLv7emCW/l20u0/8DsAUw9zhwf4/uiPGORsZjbKqBA0DaF8bZ+bjh978eQ90d1/uE9fORVm4IKQ5G3X3b3m3Q3htuOh9ogtCmse6Z7P+yAdCeh2cW/pd3yEbdsrRG1SmpnikCWG1x/u6/d9Ep8J6ZzKujdZBcgbTmdncUSMzmKB9Zcajwx8PhvH5votqEuG1ixvSzP3wq+mwxSHNuTN83rz/L28oVDswo/ekLA7p4K/s9+1KIdINjpBekVOj8SjoesUtWJsn0dft/U7wm1LSS7KVFnML7Sszto0f2+EIAneGz1/0HYZbsC73iWtnVhaO7cHT/cakT3tOSDPXfLI/r9JfFNKn/e5v0ZXI/OMdL4EI6aVgtnn4xh/dZ/bx48aDSRnDYiYbJ9nX7SP28g4p5sxs7qjBYibc/dSpfBtMQeXQvhqO1W2U5q3Pg8VMlv/EdXLhsqDRP8g2jD+P6tnowZtedCm4ESuYzu3/5Vn8R/b3R+PNu+4zb+pH/fnAZrFJ5nnt6M/JmovXPbyRyvIzH39kLqMqhWrzpWEl88JfPGjWOn+pQjDtPueWrs2ukph9/HgvP93DlDLE0x6uQDlnWVBovxLBPKF4fR5fYHh+TSKy9nSH9Kowd3hQzS46riKSeu1yAu0kQDsJ0E7CDQxpZ9h92U8swj56e7DieqLUpF67nEA7CdBOArSTcNNC2lvJJN654VrGYYo7O5Yj3dqlBdpJgHYSoJ2EmxbS3pQlb1zZW5BS6xjW9a/iuXbSrl1SoJ0EaCcB2km4eSEtKdBOArSTAO0kQDsJCGlJgHYSoJ0EaCcB2klASEsCtJMA7SRAOwnQTgJCWhKgnQRoJwHaSYB2EhDSkgDtJEA7CdBOArSTgJCWBGgnAdpJgHYSoJ0EhLQkQDsJ0E4CtJMA7SQgpCUB2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CRsJaWzYsGHDhg3burY1h/QqbwdXA9pJgHYSoJ0EaCdhpnaEtHhAOwnQTgK0kwDtJCCkJQHaSYB2EqCdBGgnASEtCdBOArSTAO0kQDsJCGlJgHYSoJ0EaCcB2klASEsCtJMA7SRAOwnQTgJCWhKgnQRoJwHaSYB2EhDSkgDtJEA7CdBOArSTgJCWBGgnAdpJgHYSoJ0EhLQkQDsJ0E4CtJMA7SQgpCUB2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CQjpJWAnvdpWqTlw5/+Fa/V/bta+04fsGvcrioTaRQDaSYB2EqCdBGFDmtnmc62kZFQlV9J0wzpzPnz4sqGEvDCkHaOezahKbhshfQnG9uBpNesdwa7lxswxe3CglVUlk688PbbHVLt4IQJq55yfGtpW8HSd+EkbFqvsXntgU53MFyKg9kVnO7SvDHOtfu9Vs3qrYThxf65ldH9qVcp143TqTQJrT39In5nNnXzlYOgyHlboZd0i1MyGnfJthPTSMPfD4cHAZpwz+327UshrhhO+6A5axZ37xojxsW08LBXbppvSEiSads45Z6PufjZ8BN5uxzoPXjkzm9+XGkc248w+ul/8vmWeUe7ofETTvvBsh/aVYZb+3d29/85m1Gw8pNmws7NbvVtQla2pkBZbe9pDmln6dkI6O+n9+yeEtDCwP/r9PwNXzDEa+UnpOrf03UgtdmpodwjFLkYw7ZxzfmY292a0KrxiNTkKzDEaedoL3/kIpn3R2Q7t6+Lc0neTIc05n5kX4msXIqRz8f5ntsHu7qX2CSF9Zc4t/e7kaCZNild+Uo03NFPUOt1+vNP13NJ3Y91RjlHPRtvZKUI87RPiZzu0r41LhbTw2tMe0pyd9GqFYDTaSb5om691rVR+Zg679WJOVXIl7YUZjGuGg53xwSHHMl62KrWO9ZfVbZSUjJqtdYbeJ3uTwva+Cdt27rCnlVWlUG12j/u/ffTOCT9aPjuW96WFqv5p/kSz9ZPu8jMf1zL0RrVxFI4ITZUo5hiNvCJS+Ukx55a+G3R0Z9RioxcWHzbslHOxbljHqGcpp1ksQDTtAVNnO7Svj8uEtPjaUx/SPEzKTCKDPfuqklHv1Nr9EePeeEMuX+uOmPfq1n73hHHmDg+q/lHxYiCjKt/uN386tsf+zBrvOsufFJYJjui5pdf2uyeMc87Ho8OX/UhIl2qPDgY24+NR994150q6y89MQu3RtJiOZIT02hnb5i8dr/iE4/3TlZRo1Va6mXm2Q/sauUxIi69dhJDmnHPHMvR6MacqGVUp17vDoOUaiVjOY7U8G3bKd/yjFetWTSRB/HhHL7vYsFPeqja7ZmLKcbyTduYoyEZJd/lZwNg2X9SLOTV7rzcaI6SvkbFtPCyFZ6n41ZYIJM52aF8jCOnVPnGTONZRu5rNqMpOMD0vEdJTB4nZ5uFPrUohcv/J0iHtt5Izanav9SoyqoeQXoGoLnR3XyOnhrYVufoUuwNQFGJnOLSvDXR3r/aJ64VZb1/Hq2w26u5PFC8I6bE9eFq9tdd69cYc/X6VljTnsd7C8IoYIb0KyR6OOxF1U1M80oTY2vm5pd8NTtrEpHrvHMa10QaIneHQvi4uPXFMaO3pD+mD/cTSIrGMnNXdnW0YDosdiat1d0e/M3rLI0J6FRyjfiu43MEtWNfHqdF4hHuBrpvY2Q7t6wK3YK32ieuFWfq2UpgMDHsLxxQfGv448amhbYWLyDD7fbvyrTdZzDEaeb9X3B8cymtvPvfff2HLh/Rpv/ubnx/spFfb8vMj3luCkF4MG3X3s+X6c+8IjYzGbmwyPBYz2RDMNg/fhKXm+HHjgTGKmBV7eYfUcsHZDu3r4XIhLbr29If029fWf1zL6Myc4O23pB/9/KzmDx4fWcE9uCOj4S022X5nfTG0LbXY6Fl/Re5L2aobnyOLJu52Br/Uw+WZyrrF/v5ovHnXfVYv5lTFL3jM0reD21ry2tGf4TTOa1woNN3lZwr3U6dS8I1Vmj0zuSaf10sxdWRTh2Dag/NfVQrV5svp2xc5s48f7+WVjFrUDqYOSnoQTPtFZzu0r0pwD85UrRtdATeTHDUTWXvaQ/oikmPSN4EUaL+JQDsJ0E4CtJOAkJaEFGi/iUA7CdBOArSTgJCWhBRov4lAOwnQTgK0kyBdSEcHJ2ZNIpAVlB8SoJ0EaCcB2kmQLqRvKtBOArSTAO0kQDsJCGlJgHYSoJ0EaCcB2klASEsCtJMA7SRAOwnQTgJCWhKgnQRoJwHaSYB2EhDSkgDtJEA7CdBOArSTgJCWBGgnAdpJgHYSoJ0EhLQkQDsJ0E4CtJMA7SQgpCUB2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CRsJaWzYsGHDhg3burY1h/QqbwdXA9pJgHYSoJ0EaCdhpnaEtHhAOwnQTgK0kwDtJCCkJQHaSYB2EqCdBGgnASEtCdBOArSTAO0kQDsJCGlJgHYSoJ0EaCcB2klASEsCtJMA7SRAOwnQTgJCWhKgnQRoJwHaSYB2EhDSkgDtJEA7CdBOArSTgJCWBGgnAdpJgHYSoJ0EhLQkQDsJ0E4CtJMA7SQgpCUB2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CQjpy+JYxstWpdaxzqn3JIbs2lMKtJMA7SRAOwkChrRj1LNzHhVS1i220e9mjtHIKxlV2UVIr4prvWvu5ZWMquRK2gvTHkdfZPbgQCurSiZfeXocfylViKedj+3B02rW09613HiBYbb5XCspGTW71x7Ymy1MKyCg9pDxqHsvn6ipoH1TjG3zRb2YU5VMvtJ+ZzmxF0XWnu6Q5jwIy626cTr5lX10v/zAcDaumln6NkJ6RdjJ68c/emWG2e/blYJabJthYLiDVnHnvjFifGwbD0vRl1KGYNo5cz8cHgxsFmjPa0ak3jozm9+XGkc248w+ul/8vmWe0e3qIkTTPoGNuvvZRHMC2jcEc832tn+V7wz1Wj57rzcKr/jF1i5kSHN+bj1/hpAWAvblfX9SWjyl4dE8t/TdSHicGtqdbX2YzpQWSztnf/T7fwYmmWM08tlGWGSYpW9PfmSO0Ug2+FKDYNpD3EGr8s96pRANaWjfFGzYKd+ZZAQ76dUmV6WiaxcwpNmJ+ZwWKeQAAAqVSURBVOHvzX8v5wjpTeAY9WxwNNmwU74dSWXxyo8gnFv63VJz4E5+3I218Byjnk3dee4hpvYzs/nPlmkZ2lbEM7RviqmK+tzSd1U/mIXXLlxIM9d81goD27WMV83qrca74a/tSiFfORi6jHPHOmpXs5n44EQ4C+wvq9soKRk1W+sMw/4/5lpvW5WCGh+0CI79zLeQIVb5SeIY9Vt+T1S8Vc2DYy1S+REA1zL0RrVxNBmIY8NOORfr/XaMejaXzj4MAbUz13xSbQ5cfhoLaWjfFNP1RuQ34msXJaSjs8bCav3U0LaCWB05ZrtUbJvu3+bjB0HKeoMTDcP5GnzIt/vNn47tMY+VH+aa7VLxoWGP/bkewfFmlr4dvoWd9GqFzU9Yuxihyk8C5hgPtv0m3cKilT4E1B4pO8VGL5xKM11JiVZtpRp30Ko8MV3GEyEN7RuDWfq2kkv2yXktafG1ixLSkZb08FWnH7a9Tg1tS40Mts2aEO69NxEA0f6QU0PbCdtzzH7frtz1ZhbEe1Gib6FErPITY1J/cYT0dRHMeg2n0ohfbaWYM/Pxo2DKEkL62vCCwO/p9G8Y8cyLr124kE6MSSdCesGg5vyQjo6SJt6DkF4nZ+bjh9HxAnR3Xxsx1eJ3AKYV5po/3u+eBBrR3X2NhPd5Zvdar57Vi8FkF/G1CxjSMWaF9OxafnFI5yLTaiLvQUivjfHo8MeDxIh+Yk7m9BSPNCGm9oCY6sSk+pROkPQQSnswAJfcvEiA9msiPp1beO2ShXTQ3V3UDsxgooz7yTD/XhTSbNgp51SlXO8Og5w++2j87iCk18bYNn5sG6PwIA2fv+gHEy9xC9Z1EJmvx8W/KUUQ4i1paL8Wpu+EFl27dCHNz8zmTuwy1l8fY8GYNHPNdil25bvTMs8WvoUS0cqP48+Nn7lgHBYz2Qxs1N3PluvPvdVMRkZjt6p/ivQVib28gyAkQxraN4t/s8/0mmJia093SCdmgSUC0m8BZ1Rlq1Tcm3RfhCvATW7BOrf03cg8ss+RXikvgydLyqlFrWNY7sVvIUOo8uPNlp/Z++fjL0M2a8XQVCGUds7dTx3vlkIlk680e+bUUojMPn68l1fi3U7pQzDtMaZDGto3g58U5bpuJJe/9RBZe7pDGswC2kmAdhKgnQRoJwEhLQnQTgK0kwDtJEA7CQhpSYB2EqCdBGgnAdpJQEhLArSTAO0kQDsJ0E4CQloSoJ0EaCcB2kmAdhIQ0pIA7SRAOwnQTgK0k4CQlgRoJwHaSYB2EqCdBIS0JEA7CdBOArSTAO0kIKQlAdpJgHYSoJ0EaCcBIS0J0E4CtJMA7SRAOwkIaUmAdhKgnQRoJwHaSUBISwK0kwDtJEA7CdBOAkJaEqCdBGgnAdpJgHYSNhLS2LBhw4YNG7Z1bWsO6VXeDq4GtJMA7SRAOwnQTsJM7Qhp8YB2EqCdBGgnAdpJQEhLArSTAO0kQDsJ0E4CQloSoJ0EaCcB2kmAdhIQ0pIA7SRAOwnQTgK0k4CQlgRoJwHaSYB2EqCdBIS0JEA7CdBOArSTAO0kIKQlAdpJgHYSoJ0EaCcBIS0J0E4CtJMA7SRAOwkIaUmAdhKgnQRoJwHaSUBISwK0kwDtJEA7CdBOAkJaEqCdBGgnAdpJgHYSENKSAO0kQDsJ0E4CtJMgYki7ZvPbRQ8MudU0v67li/7sVW6rSkZVble7f67lEzdHWssPc61+71WzeqthOCz5mj040MqqkslXnh7b4yVfShUiauf81NC2gvKS29aH4V9A+6q4ltH9qVUp143TqdfmaufMNp9rJSWjZvfaA3v6gKWE9Gr3GY+69/Jl3YoYXHRKi6w9/SFdq3eHLueRHP2hZ3/lfGwPnlYLF4Y0c82Djule/FWOUc8ipK8Os/Tv7u79dzajZqfSwh20ijv3jRHjY9t4WCq2TZdd/FLKEE8752zU3c+GF7W7HevcfwHaV4QNOzu71bsFVdmaDum52vmZ2fy+1DiyGWf20f3i9y3z7Jp3fElSqj3ANxwN6UWntNja0x7SHw3T8f+dCGnO+Xj0y5uPi0PaHbSK5dYyIf3VbN1CSK/IuaXvTqXFuaXv5jUjOI6nhnYnaFsseCl1iKadc35mNvdmtfOgfT0wS9+eEdLztHNm6duTw8Qco5FoC6aHNGvn7qBV+We9UoiE9KJTWnTtKQ/pKNMhfRHup06loCrfIqSvi1lpwYad8u1IBkQKyYKX0odg2nnQOVTUOt2+5S53RNJHirXPCel52r3DFPXsGPVstJ2dIlKs/cxs/rNlWoa2NZG56JQWXrsEIc1c622rUlCVjKqU67phuYxz5lrdejEXGcD23sVcq/9zcy/v/bKoHZjB+ARCeg3MSIupiow5RiOv7Has8wUvXfN+L4NY2v1fhud/sdGz/GYGtK+LWSE9Vztnw045F2nteWmRS2cfRlq1M9d8Um0OXG/UP4jeRae0+NqFD2l/cKLYNl3m/TtfORi6jHP+1Wx+o2SiLWlm6dtKJq8ZjjfvIDpihJBeA9NpMR0A4W/+M/8lpMWlmNfdzTkf2+YvHa2sKn4ZWXhEoP1yzOnu5rO0z8oG0dKCHnfQqjwxXcZjIb3wlBZfu+gh7c+i/MabQMaGnXIunMoxI6S9RM82DIclX0VIrwGENAkLQtpjbBsPS365QEivjfkh7RHVjpBenTPz8aPeyJu2jZBe4RM3xqyQTiar/zdeZk+HtI9rGXr7kXY3j5BeM+juJuHCkOZepeZ1+kH7urgopHlUuwT9rqQw1/zxfvckcIXu7hU+cWOsJaQd66hdzRb2uydjtKTXz7yJY3ci5Scyj2PBS+lDMO0z/uauXzFB+5pYIqQj2pMzkL2349poSaK3nke33LY+ZItOaeG1Cx7S/pELLov8oJ3X3c1cs11S0N29OXALFgnLtaQbj4I/gPb1sFRLeqJd+HuB0kSsJY1bsC73iZvCH29OLA7A3OFB1Z8s9tXL4HDimDdNTFW26sZo1H//hYXrl+12LNts7qjRkPYXM0lpN0iUFJefOWmBxUw2y8wODNs8fGN66y4x+/hx44ExmrwM7etgRkgv1i74qhppIhHSWMzkMp+4Ab7a3R+SvRyVru2/Gr0Fq1Btvo3cm+gM9VpeyajFh4Y9DhPdu1NraL29X8ypSq6kdS33/wbN9Flj2CkjpeXHv8qZtRQi58x+364UVCVX0l6YyWVB576UKgTTzkZGoxwUipeG5STeB+2rEe99ndywe4F2zuzjx3v5xP2f6SOt2kOmQnrxKS2ydiFCGsSAdhKgnQRoJwHaSUBISwK0kwDtJEA7CdBOAkJaEqCdBGgnAdpJgHYSENKSAO0kQDsJ0E4CtJOAkJYEaCcB2kmAdhKgnQSEtCRAOwnQTgK0kwDtJCCkJQHaSYB2EqCdBGgnASEtCdBOArSTAO0kQDsJCGlJgHYSoJ0EaCcB2klASEsCtJMA7SRAOwnQTgJCWhKgnQRoJwHaSYB2EhDSkgDtJEA7CdBOArSTgJCWBGgnAdpJgHYSoJ2EjYQ0NmzYsGHDhm1d2zpDGgAAAACbAyENAAAApBSENAAAAJBSENIAAABASkFIAwAAACkFIQ0AAACklP8PEXq+Ph8OfwQAAAAASUVORK5CYII=" 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>
<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 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BIVLAOAQgAKASgEoBCAoUtUsAwACgEoBKAQgEIAhi5RwTIAKASgEIBCAAoBVKHLgwcPHjx48FjsMTd0lx34JP+wDAAKASgEoBCAQgCGLlHBMgAoBKAQgEIACgEYukQFywCgEIBCAAoBKARg6BIVLAOAQgAKASgEoBCAoUtUsAwACgEoBKAQgEIAhi5RwTIAKASgEIBCAAoBGLpEBcsAoBCAQgAKASgEYOgSFSwDgEIACgEoBKAQgKFLVLAMAAoBKASgEIBCAIYuUcEyACgEoBCAQgAKARi6RAXLAKAQgEIACgEoBGDoEhUsA4BCAAoBKASgEIChS1SwDAAKASgEoBCAQoAch+7EbN+C/5xht29PpHTN1p3gK3fapnuBn2nr9eCnrbbMySJP98Rs3dVK272hc9WftMSTvDDZl4Gwf318r1woaoVqUx9e5MNeCtkIcS1D/65dqzaN4+QLjnXQqZeKWqGorTf2TVukfmo5EyJc6+d2raIVilqhUm/9bLlpK8n+kkkwts0XzfUVrVAs1zpvrCu3ThcnUyHjkX6/XO1aYRW41puW156sbDRemPY4/XPKcehKKaVwjD1P0GZ3GL96xEj/63/qo0tcUGLYq64sPs+CLsJifuySTvLiZF0GJ+/1V7/aYynH9uBpvbQ21cimTQZCxLB3d6v+RUUrwNsfj14/7RxYrgy7Jnfb5knKZ5cnIVKM9J1Spd794EopxcjYq5YbRso5k/UlE0e4Zmez9vRXeyylM+xul0v3+6O0YyZDIWKk75SKWhi64uiHx8+8noew33ZqFW29Y2bdLctb6MqJ2VotFLXC7br+EV745snlAuljv3Y71yNdKZd2khcm2zIQf7w9jNqIY6Oxln4bCmQlRFjdTcgY8c/Dw49RgyGGverKzcmYGULkqdXd0kp7hiOi74n9NR1y0nJK6ZXEZ5EicdTfrtycCpHuoF37slmrhKGbbE9mllAaMHTzSV5OMidlIKXXgnye/kgOyFPGANl0SvIkxJsYC4f7wjH2Vm+MkGmE1d0sbPWs0+AL2ClJh4yEnJitL9umZTTWtPj0chzHaGYxefYJhG60xLv6N/1/nzc2ptf/hG1GX/+ph3kWWwcKF8aiFeU7bXPkrZx5LZo/LxFfZo6+2TvPia3vJleji1o0sROuwyUXFc44yWzIRxkI1zJ6jd0HxmXWExZLnjIGODYa1R39KGVF+RLiDtrrK96Ek7APvmo8+zX1Rbt8XDIy6ILEQ3f6K2mQhRDhmk/qrYErj88I3VvZz7dfx9CNVkC19YeGfRosA3u7rqTfvyt4kektDcYXX4U73K+XiuVtfSS8nqD/MQiru1koaoXKXxov3zu/96or2q2WOYl9iq71pvXkB++3+LufwtB91DZP/GX8xJq0M+xulwuVHf1IePOB297KtPokMyMHZXBsNNY0f+ODnv6+GCBfGRPHMZrV7BeoUmOekKhPPK+pXTI5uGR8hNXdTOyGEY6xV74JI1130K49MV0hVaErHOOrzdYg/b2Zn0ToJidjg38SbGx2jGapGNtzATO3Xpvu/3zv3/ov+TnqVe2p1d0qNwzH/+dTO2khdA9/sUTQ7y4Uo+V6/2Ti27DvtE33rJPMjJyUQTgNEPRRMiNvGRPgTaZlMPeeOyHusN9qtRtVrbCysXeQ/n7uvFwyUvqNW7DRRNiD/UY1/b5I6kJOzMdfB+PX+aEbBXPafPqhGwxYw5uLknk248akolbTbRnmKK4buWZno1DELfiJ0PXwB69abE9pcG7x43Zd/3jGSWZHTspASpnVihSQu4yRUkrhms+a3pbd1MmXEPdDb7vRH42lHNvGw43CykbqQ5k8XTKxO2RK99qvvm2u34bbQFIgXSHCNZ89iBZZ5oXuifn44YI2vV6Yaxu6zi+91+FXVKGLA9/ZoYu3JEkZ5uiMW4H9PmOhGG1Xngpdf7d6cnAWnAwuq5xxktmRkzLwyGQzKpCvjPFeGv3UeZ5N4sp8CTm1uluxFtbrH9+EJcxzkdXlk66QcDUKjngLPx69frafUeLK/IduMO8K8SMco9OJsvAy08v+Ps9gPXjGvOX80JVSBl1pmIsOQzf47MMV4tE/3v9rEq4T44YX9UlmR17KQEp/Myqnl+HrttF5bNhhzAxf9Q5T3Y2ZJyFTwxrHaJYYulJKKeyDB+vZbP7PVMj0SHdsG8860ZZMZ/j8xWGmi9z5C13v/tdCUSvd6wy8tmVsD541/29stSYMzobhRM/TCMPS/wnlbX0kxvbhk/pnK7GdxuFeJ/+eemGbfzdtEc1Lw4X98YfWk773DSN9pxTEZ2IBOJyC9me3hP22U/vvvj3xbpWLDZHHtmmY9visk8yMTMtgPNLvl4P95MI+eFDdzWpGKCRPGSNcS/ceNhQ7bkrGzBZidjaCC9nbtJh+Ly03LWeAaxmvWvVbYfuZNnkKXcfS9zZgEJz1IncOQ1dK6VhGN2pcSvfaevx5d/GnQt6utx7VI6HBBubYwkZn8O777d32K/2H6GfEnqVXutf2HvGTWOuNJ9/o0LAcv7GrNp8PbAHffKc9+OAna+KWoWBiJ3oOWXJV+IyTzIZMy8DfWK75j/TTM3lmG5CFkOSMWXinf7B+kasWJBVmC5FSxp96yMdABvNn1WbXyHDbf25CNxxfzZt2TolrEbokM1gGAIUAFAJQCEAhAEOXqGAZABQCUAhAIQCFAAxdooJlAFAIQCEAhQAUAjB0iQqWAUAhAIUAFAJQCMDQJSpYBgCFABQCUAhAIQBDl6hgGQAUAlAIQCEAhQAMXaKCZQBQCEAhAIUAFAIwdIkKlgFAIQCFABQCUAjA0CUqWAYAhQAUAlAIQCEAQ5eoYBkAFAJQCEAhAIUADF2igmUAUAhAIQCFABQCMHSJCpYBQCEAhQAUAlAIwNAlKlgGAIUAFAJQCEAhgCp0efDgwYMHDx6LPeaG7rIDn+QflgFAIQCFABQCUAjA0CUqWAYAhQAUAlAIQCEAQ5eoYBkAFAJQCEAhAIUADF2igmUAUAhAIQCFABQCMHSJCpYBQCEAhQAUAlAIwNAlKlgGAIUAFAJQCEAhAEOXqGAZABQCUAhAIQCFAAxdooJlAFAIQCEAhQAUAjB0iQqWAUAhAIUAFAJQCMDQJSpYBgCFABQCUAhAIQBDl6hgGQAUAlAIQCEAhQAMXaKCZQBQCEAhAIUAFAIwdIkKlgFAIQCFABQCUAiQ49CdmO1b4X/LUNnRj4T/gmu27gRfv9M23UzP8mO/dlsrFLXC7br+MdMzWQrZl4Ec2+aL5vqKVqjUH7+1xdn/YKlkJMSxjNfft+6tNgwHXnEtQ/+uXas2jeMsTiwLIa71pnWvXChqhZWNxgvTHs/8LjHSd0pbPes05bPLpkLmlsHYHjytlzxXuuVmcP1k2oaMR/r9crVrRe/bsQ469VJRKxS10r32gZV+fuQ4dKWUUjjGXtnL19L9/ii6usRI/+t/6qOsm2AppXSMZomhuySEa3Y21h8a9liKkbF3d6M1yLaTlYWQU6u7/Zfa5+VCsQyhK4a9u1v1LypaYe2mhK44+uHxszeWI6UU9ttOraKtd8zpLBFH/e2KVrgZoTu3DIT72+v9gS0CV1g/qZBhGyJG+k6pqEWhOx7p98ul7d7Qq5+DB+ufpX/h5Dx05cR8+tfG/Y1CUSsUy7X9YXh1TcxvnpiTTM/Nxx+RM3SXgBj2qrGrwjGaWYxd4mQmRAx71ZWZjaawups3JnTFH28P453v2e/9xGzd/z+NL8o3JHSllDNViH8eHn4MWkzhGHvl0p7hpD1SyeyScQft2pfNWiUKXbyITq3uVvodkfyHbvcbczTsbvuzSeFAh6GbCtmWgbC6m4l289hofLbZHWY4wcHQBTJuKByjWZoa3plP6q13I2PvpoduglOr+0UmE0UZCTkxW1+2TctorMVGusdGYy02NXJsNO5ypItMzO43pivFyNiraoWiVrjbNk+8F5KhG5upX2/0DH+mfmK2Vr3Z6Vst88RbClprGsfR1wvbPePHdq2iFYra+kPDdm3j4YyBtXQs46X/bbCSxNBdFqdWd0tL9M2Pk5dQBjB0gexD91Zi4Um6g3btielOHIZuiGsZ3b363kEmWyKyEOJ1vAYuthjCNTsbftt+ahutZhbbRK5J6Eop3Q89Pxo7piuSoTse6ffL/jjY+3Ol3v3gSuk33IWiVtpqvvqHY3U3C8XVljkJv+59p78CVCyv3/lTabv37lWzVNQKK8GgyvvmtaZxHKwVxdYJGLrLYjpiGboM3TjCMb7aTIzevPHNSbAdhKEb2xazvte30l/SzWSrndfxErNajGhnWVZzZtcndMNV8UKxvK2PxrHQ9bcy+TuZhdXdLBSDEdLE1ne1QtHfUhGtEYZf3+3bk2hHtL/G7u9JXm15v8ILcm8bS/Cdt/zXGLpLg6Ebg6E7TdS2egjXfPbAv82BoRsnuAUguR01HVIXcmI+/jp4m9MthnCt1+3W1831Fa1QfWBksBn3OoVuODmgFSo7L7/rPAlTz5sr9uJTSluvR3cTBeGKOwjmhG5Nt6WcCt3gt1tGr/Wo6Q24GbpLh9PLMRi6yIn5+KG3DdXHHXT2XgeNKEP3wt+wJNIVEu94yakWQ7jD/R3vthd/yTJYr0yR6xW6Mhx0xhPxXKF7q5XcdnXB0PVuDSzd74/+zZFuagiruxkPXTHsVW9zIxW+chNDdzx6/Ww/nrjxeVQ40u2l5TZ08V6AtEhXyLHRWJtRA95kMjYgJ2brbvqd+GsXutI3FU9Ef3rZ79X6GQzTy1cKXf83cno5bXjLUAhDN2JsG8860cSgM3z+4hDvhOFId4rpTWepkKMlKsdoluJLucIx9soM3STjkd74azRXECCO+tuV2NyvM+xuB5unvICc3kgF08vhRiovdIP+kfcBiGGvuqKFzyIIn41V7VrOoL2+kghdP/IzW5ZfKlmXAR+OEcDQ9XEsfW/j7LEsQ9fbBFNtPveejjEy9raCVjFVchS6XjoED8eQ7ode7c7OdL4smRyHbvwxkDhOldIdfNP9bfYtQ7GHe8VuDYrNP8PXbz3qv9wNL+DV1sv/8Z/sGI5fHf9G4fVGz/hg+fcUVZv60I0eA5mHZ1IunuzLINptGDQfmZLJ/Q/JiVO4cXlNmT1LJ10h0eoSzhzid96o0J1TBuEdH4Viudbqm9lcPXkKXSmFbT5v+J02PgaS5BCWAUAhAIUAFAJQCMDQJSpYBgCFABQCUAhAIQBDl6hgGQAUAlAIQCEAhQAMXaKCZQBQCEAhAIUAFAIwdIkKlgFAIQCFABQCUAjA0CUqWAYAhQAUAlAIQCEAQ5eoYBkAFAJQCEAhAIUADF2igmUAUAhAIQCFABQCMHSJCpYBQCEAhQAUAlAIwNAlKlgGAIUAFAJQCEAhAEOXqGAZABQCUAhAIQCFAAxdooJlAFAIQCEAhQAUAjB0iQqWAUAhAIUAFAJQCKAKXR48ePDgwYPHYo+5obvswCf5h2UAUAhAIQCFABQCMHSJCpYBQCEAhQAUAlAIwNAlKlgGAIUAFAJQCEAhAEOXqGAZABQCUAhAIQCFAAxdooJlAFAIQCEAhQAUAjB0iQqWAUAhAIUAFAJQCMDQJSpYBgCFABQCUAhAIQBDl6hgGQAUAlAIQCEAhQAMXaKCZQBQCEAhAIUAFAIwdIkKlgFAIQCFABQCUAjA0CUqWAYAhQAUAlAIQCEAQ5eoYBkAFAJQCEAhAIUADF2igmUAUAhAIQCFABQC5Dl0XbN1R/V/NdxqmZOF/KKP/dptrVDUCrfr+seF/MRPhuzLQNi/Pr5XLhS1QrWpD92MzyYTIY510KmXilqhqK039k1bxF4T9ttOraIVitr6Xt9yUj+3bCtkPNLvl6tdKzKicpUOGQhxrTct7xpZ2Wi8MO3xuV5Ki+zbkJyR89DdDtrZMBd3+/ZEyrE9eFqvnBm6wjX3e+Y5GmrHaJYYujPIugxO3uuvfrXH/ideWmsax5meT/pCxnsh9IMAAAUVSURBVKPXTzsHlivD/sfdtnniv+j+o//8nS2Cl0p7hpN2ymRYIWKk75SKWhS6SldpkbYQcfTD42dvLEeGPbD1jumKM15KkazbkNyR69B9b5hB1x1CV0o5Hv3403t16LqD9nq1fZ7QnZjtWwzdGWRbBuKPt4ejsG9+bDTWyg0jg9FcjNSb1H8eHn6Mmkkx7FVXAgmnfxy+G4WvOUYzi05JZhXiDtq1L5u1ShS6KlfpkbKQ5DUihdXdLPhloHgpTXIQJfkiz6EbZzp0z8L90KtVtMIdhu5VyFEZiGGv+nn6AxcgayFzex7C6m7eoHHMidn6sm1aRmNNS0wvx8mml5ZxhSj6XjetW5ZXrnvoJpZweoblSimlcC29ub4SWwD2/pVjGS/b3gIYrHAwdOeQjzIQrmX0GrsPjFH6S3RA1kKOjUZ1Rz9KenAso9usPTJuyoqdcM0n9dbAlcdnhe60q6WTfejeut8fzaoExUvLJOtLJndc69Adj/T75cLKRmvg+n+u1LsfvIHtxGytFoqxke6p1d3SvNkVcdTfrmiF2GoQQ3cOOSiDY6OxFvSTdCv1kRyQfZNaTQ5n/e0ImW00y2Lf0KBde2K6QqpDd9pVKmRaIcIxvtpsDWaVgeKl5ZKDNiRfXOfQ9ZsbP1aF1d0sFLVgL8lU6HqpXCw3DCfcFx3uf2boziEvZSBs83ljo1Asb+vZjnYzFeLNqc6YYBf2YL9R1QqVGzCwOzEffx0M1xShO9fVssmyQqLuyEVeWjJ5aUNywzUO3SBWg6/Yej2WslOh6yFcy+i1HjW9SWaG7lnkqQxOre6WlsUG3TjZCRGu+awZTOTMev0m7BsSrvnsQdSxmBe6Z7laJtlVyIn5+GFvOPPzV7y0dPLUhuSCmxS63i1rpfv90b850j0nuSoDYXU3b2roitFPnefqFDm1ulufeuiGaw1wrGx2h2FZnMPVEsmoQsaj18/2Z8eq4qU0yFUbkgeucegG08tbPetUhik7d3r5xGzd1Ti9fEHyVAbCMfZWb+T0srCNzmMjeNCDcIeveofTe1Bv4L6hGSPd87laIlkIGdvGs060zdAZPn9x6PdNFS+lRJ7akFxwTUJXDHtVbzeyH7FSSimdYXc72DzlZWq0kcpf4i2sNY3R6PDtH2MvVotatWs5g7a3tzkMXT+/E/1lIvPwvKHguULCPnhQ3c1qiiwkdSHTW/GDq0Ac9bfXgk34Y9t4uFnbH96sfUMQuvNdpUjqQhxL39uAob/vRPFSeuQrSnJA/kN3Yuu7OJtU023/1dgtQ6V7be9hNMFLw+52uVDU1h8a9jj210bP+GAZDzeiDZ/hMHp6Dfimk+1WTHe473+4hUq9pWfyEDsg7UcfeA9dmtOk+iXtFb+exTMP8xS6Slfpka4Qf3/orMl2xUupkpsoyQv5D12SJSwDgEIACgEoBKAQgKFLVLAMAAoBKASgEIBCAIYuUcEyACgEoBCAQgAKARi6RAXLAKAQgEIACgEoBGDoEhUsA4BCAAoBKASgEIChS1SwDAAKASgEoBCAQgCGLlHBMgAoBKAQgEIACgEYukQFywCgEIBCAAoBKARg6BIVLAOAQgAKASgEoBCAoUtUsAwACgEoBKAQgEIAhi5RwTIAKASgEIBCAAoBGLpEBcsAoBCAQgAKASgEYOgSFSwDgEIACgEoBKAQQBW6PHjw4MGDB4/FHrNDlxBCCCFLhaFLCCGEpARDlxBCCEmJ/w9YV93OzCcTywAAAABJRU5ErkJggg==" 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>
<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>
<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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ES62aHew2pcXl6eCsQ6i3IjTfxR+lUpqrOoUffHjRsn6ViiLln6NXK2mg7WKYu4ngbeNYFy6CSFau2XmWANjrGIMenF4NDQTkwot2zZQmPHjnWg8inU9Ye9qCudp8pXV9Oe7BmUd7MzuiVM4xAMb6q9fJh2HJxAv8xRSFIq0EXZMBuQ66IiiaEoKTcNoDt8YTpYfT6Gsj6NBt8iTVANlaEnMcYixqQXAxOTyl7FCghEZ4jQToSUG3pROhFdN3Y2+cfdfO20yMYK7d+/n+677z6DJdbTgTX/QX2WPkaZOnVk2ENn23Su+zAa/2gqHfnwL1TXquuOUGPtCTqSM4HuGni9QTz0JZenc15cnWNiUjkmQqGQtP3Euc2636NbCkvopRkZmqc+KpuoKhoMKuEsX3+IUOOBP9BbvWbTLzJ76M5m2LBh9MEHH+hOry1hb8qeM58mvrOI5q87Kim7I3UfUen60zRv6WQa5NBThLGIfYSeXJ2zw6xKaTxlR5lmlwGDNhhWOhIaPhYl/g2iqqHZkeKjC0VfGjFwbK79kyhZd6TFUDQ6Z23fUQejddFWIg6SfFcU5+NUZhLXHjKpLSczY2NMxjuzz8yyrMxLyREOcb2295UbYuPtDGdwtoXG/fTKPWPo/77xR1r+2wr6+1//nIbonPaYVWf4BJo9e7Zu5X+kbjf9y1vX0z8+Kkt9EWo89kd6Y895zVWEtIC6wDGdPSGFug0aT8+uP4LdEiTef5mmZzpraIl2Y0zCdMNrgYlJZY9CvwQPjbaFSCOdC52iitDX9Pf/Z6ZuXYyZ9YUXRRj2aQ8Rajy+lQqnTqN58+6l1O/BQBGf79ENt79FlKpPeQyzDdQpmQOMLTE2vRau81qDrGgPJAVYHNuqX+o+jl4Oh61oju48jx07RiNHjtScPvL5Nnom+yF6o92SOxEZUB6np6fT3r17NdfHawkgOWKMqt8e5H4EWGJS0UfwzuilTlfR5JhRTp06RQMGDIh5L97FlJsnUym2omAKpPzsmKlbedynTx9CnZI93HbbbVRdXe0pGNjtiYrulE//kN28qkjiySiYfjU1NdkrOXaCZDt3GZ3E9+JtL4xPZT+yxKRipGIK07dvXxUxvRtFtpWxdTqrAs5Ro0Z5dluGiuZLUTA2YcbhpcDEpKI36+vrCdOGZA5Y/YLNjNsC3KCcP699Vc9t7TBSHy+OTSYmFSPi4sWLKmJxFEbAGQTgTRXKby8FJiYVvWm7qYCKOtkdBbolN4Zbb73Vc4pfrThj7yDc8XgpsLmAyt50m25FZbVNi3by5EkaPXq0rvygn4pnCIk3vt5NwdjM29ho/+5+XUBwItUIMDGphoojxkNAJh8YPMKR25kzZ6QTij/55BMpWTz9FKYh8hsfNjk9e/aUSBBK3f79++smrXj15XvuRoCJyd3949ragYiwsbm8vJx27dolEQvIB1skYPMFv9Q4cgnHfGsJIClMGyGhwXgS3gxAWsgbXg2GDh3KRKUF0ASNy3ZMKjpOaWOhIonnosBW5sqVK9K2HBDGggULpL1qEydObCUjqxoNz6FVVVVUWVkpkSDKgU0ZHMaBuOTfVpWfCPkm+hhV1p+JScWoU4KmIomnokCKgUthLAJAcsH2HPgCckrvBgdx8MUEsqyrq6Px48dTYWGhY/VxQ2cn+hhV1p+JScWoUoKmIoknouBEGDi8x+512AthO8ovf/lLV7Xtd7/7neSP6NNPP5X8kE+dOlXz9NFVDdJZmUQfo8r6s7mAyoEgWz6rjJ7Q0UBI8OkNKQmncWC6BKW0G/djffvttxJZvvvuuxLmOKUWZ65h+schcRFgYlLRd5i+xFvuVpFFQkTBlO3xxx+XCAlt3rZtm/ojmhxqoWyVDyU7Tk/Bse0IIKgNGzZ4+lBIGXL0G14cXgpMTF7qTZ1tgTS4dOlSmjZtmnRmXkeElAgW8NEEBdMFOOyHBOj1ABMLLwUmJhW96WXr4oMHD0oPb/fu3aXleSzzxwpudUiG6WYsB34gqGXLltGaNWskCdDv93t2ege3PD166PefHqu/nb7GdkwqesCL1sWQkpYvXy7pjzZu3KjK35S8k1+rbZIKiHVFkfV+8VYH77jjDtq8ebN0zNGECRMkosI1L4UvvviChgwZ4qUmOXYKUEKBmJaW5im3Elhuf+SRR6Q+wEOr1gme23byq/V4AOLKz8+XSOmJJ56w9bBMOwY6XJ54zS0PT+VUjJzevXtL2ytURHV9FOhbMPXBsv/8+fM12f7AqttNPraxSohpttoASQnGoTB/gJJflrjUpndrPCi/sXXHS4GJSUVvYoMp9nwl+hI0Vqnmzp0rrTB2pEuKBwd8bMNpnhkh8vlWmpX6U3rj+De6s8MDqVbakwuB9LR27VrpUAUoxu06zVcu3+z/IFds2dG7Cdrs+piVHxOTSiSxfI6NqYkaYNuDI6hgLa13EOOtLG8BMYRD5DRt+82i2IcTaMgYe/T0+CBHETAtWLJkibS1JZHJCfsVMTa9FpiYVPYoXH4cPnxYZWx3RQMpYfqyYsUK3aSEFoHQ4DnAmORYTwdKiunD3sPIZwAm1AGSglaJKbpISI1YAMC+O6xOJmLAmLT1vEObQGJiUgk0Ol92+q4yiSuiRZNSvNUrtZWFRTg21OoLOB58A62gaTRvvDGdCOpQVFSkrxpRqcaMGSOR05133pmQXiAhBeO4dK8FJiaVPYo3s3FpQWVhJkUzm5RQLZwrp/sst8YgrV5BNOcXI+kGg21EHfSccRerWJAT3LfAwDSRpnWQGrGx2mvmD+gjJqZYI7WDa5AWgsFgB3fdddkKUkILQQZweaJ9RaueDqzeRDQn35RThWGdbhYxoV2y5IRpXaKQk1lSo7tG7tXaMDFp6BWs4mzZskVDCmeiwiQAK3Avv/yyJnMANbWFcSX2ZVVUVKiJ3hIHU7g/UCBtLs3LNG6hDH0Qjio329AT5ATndlCMaydeDXCYFBU6NoxJLwYmJg29Ch9EUCIbU/5qKFBHVCyhwyQA+jCzH1y5OlOmTNE2nWsM0tqAj57K62+KiI5pF+pgRYDEBE+ZixYtsiJ70/LEGMR2HIxJTwZhQyDCydDeCCtXrhSBQMCVjWlqahKjRo0S5eXlltYP5aBPL1y4oKKcZnGprFD4iKQ0SNfuk1MqQs0qshJCaCtbXZ7KWChj9uzZYv369cpbrvmNMYix6JWg5AhbGENZaCKDGQqFRG5uriubUFBQYNtgLSoqMkDQMllNEaWhrzVhuWPHDoGyrQ4gXZA8+tuNAWPQrXXTg5eSI3gqp1EOlu1m3OZKY+fOndJy96xZszS2SF/0hx9+WNJj6UutP9Vrr71GDzzwgP4MVKbENBg2Tlipc5u+SR578lhU2aSEisbEpKO7YGkLl7NuCdA3LFy4UNqcaoatkpp2yQ+F/JCoSWM0jlyWXcvjUIZjJRYE5aYgnxrjpjqZXhc9YpfWNEoxTWt6N8Z3kyiNKZwT+hDosuyc1qIsq/VnyrEm6+3cMm1CPTDFRL28FJQcwRKTTqqH1ATjNqcDls6xEmfVKlW89kGiQJAlmXhxjd6Ty5DLNJqf2vSQQLGnDo7m3BAw5mDSYJdk7FSbmZh0Io8HBIQgPzA6szGcbPHixYSPUwMVBI1la6sDynBqsyr21PXp08fxLUkYb/jgLD+vByYmAz1s10PZURVhqwRdj106l1j1AEGjDlbuI4RiH8Rgt7QU3V709UsvveSoIhxSG+rh1EsoGg+rvzMxGUDYjoeyo+phpQgPihtOx0AdUBcrDE/RTij29UlLl+n4e8tpemoXwrllXVKn0yvvHafGjkCNcx3kCw+e77zzTpxY1t0C8TtNzta1LkbOdijQlIotO8q0q4yamhoNxobm1QoGdlB6uyVA+W6FfRHy1GdI+K2oDTwlfL6ZorTqkgRTc3inKMz+sfCXndMFm1OKZ9mmCmPNq0HJEWxgaUJPO0ESbloVBITy6lVlZaUJiF7NAnnpXoFqrhKlOT7h85eJq7SEPL8WodIpimvaqouXgd2W/06tumpDxlhsJTHxVC6GFKn1EvZX4cw1K/Us0XWCwh1ivWxLFH3Pqe/Qe+CoJDj7N2NKhykc8kKeunQqKb1pwB2pVLf/EH3aGGmBpZFqQ0306Phh1F0nUJi2YoO0XUE2nHVi1dWuNsYsxxjPqUutZEN1qRIrljyls0Pcxj4uu+151PYGpnRmTDGRh74pnFzTZtEQLBHZRMKXv05UNXwtwmXFwl9SLsIq9+XJOSn/Q1o1UzJU5i//tnNMyWU69V/JESwxxaRr7RfhdnbHjh2Sm1YrtzBAGoGHA7fuKsebHdKjEakCkifyMLa9JoW6ZT5Fmz5eRfe/N4NuvyGNZlRPohfnjiGfwVGPE2b+/Oc/ax8kGlJgDMH9CsaUXh/tGopzX1Q7GFLJhnaU6VQZeMtDorEqQCIxJkmgZmdEID+9ZZf/g6I4eFGI5rD4uCRf8gKQXhwU3xlogKys1SPVIQ30SuZIns2iIbRNFBe/KPzZPkGUIwrLaoVBganVw4GV1tfGJUYDHehAUiVHsPLb5E7AYAUxGSeP2BUzcxrRXBsQM30kfP4/iJ0li1tXr2KXrO0qVrAw2LQQDOKClMyZJjWLhqp1YuaTAVELJmquFWWFOYKohYi1NaddbKwW6iHedhnFuCC/3KwkvhjFOnqJickG+K0iJ/nBNa8J50SZP1MQZYiZgWrDkoSyXlqkH7ltpj3s0qpcusgprYpq10URLH5QkAb/T8o2yb9RTyvMI7Dih5dPMpESMGVikkeWxf9Nf9CEkJapzZXE9PtFUgsf/Cd1NjWTsTJ1Gf5SmfD7fApiammvCcQE4lA+TGox6SieFiLvKI9Eva7EkqdyFvak/MCZJQVA72DONEdudIsRIikfYPm+Of9Bph2Rk4yRuYSLerdIR1EGlqLhiCjNzzZNOsSU3az+SGZSQm8xMZnzrKnOxcwHD51npogPHdOTM+eJedlKQ0TVzVMdEUp7JTmZiU3MijSHRXCdXzIZAHbkyxfFO0OiIWZk7RfRJnyMBkiKSmyM5plo6ZmYHOgxPIBGFeJQJpu62tdcLQJP+kWg9pJkDU2+QlFW+5EoKdx2VVlsAU6yVIC2yKSEqV6iBkhLRm224kmTiYqLnnozMelBzYQ0skIc5KJH6sFb1ZTpzndBUZxOgrILRSCEzRqyIaJPZPsDItRgdDE9PlggJ0l6IbJsVSt+Dcy7a0TPhLQgNb3jwbxWuCMnJTEZNDVzn12WW2uEbRUrVqyQzkN75JFHNB+qeOzYMXO2oFyXSc+eECTeX0qTB2FjBgwR59L7IkzvvzyZBnWzdkhUVlZKGOBcOHy30hjV6rGAPs3NzdXclzhQE2Pg1ltvlcaEri03VjfO4fytHYUON85txWMAwpoXlsP9+vUj7INSG06dOkUDBgxQG9118fAwPv7445LV+kcffUT4nDlzhubMmaP5wXZT47Bf8fz586qrhD5H32MMYCwwKXUAnR2CnFJMs6NMt5ch650gzqs5nw0Y6pkCugEH2WQgljkArqFtse65oe6d1QH1VlN39DH6GjZK6HsO1yKg5AiWmDogbKsvY/8TpnYZGRk0YcKEuJ4J5OlOor1dZSkJx6pj/xu8MCgDrtXU1EgO2CBRIU0ihW7dulE4HI5bZUhJ6GP09ebNm5Nz71tchGLcvJa3rPmlZENrSkncXGXpCW9TrFgpA64ZXf1R5mnlb0h28mqTGmlCrgviYtkcaRNFOozXN7iHPoWCO1a/yu3m/+3tmFhiikHWdl+C9LR27VrJfSz8OuMDp/OJFiDZQTIaO3asVPV33303ppTUUbsgPSENAvJAXrK02FEaN15H36EPcVgmXAKjb93kO8uNmCnr1AVsrbxo9m/4W7ahGLOr7Uh+eBDhVxo+tOFjeurUqfTll19SMBik+fPnO1KnzgqFK5a3335bOnATdYZC26irDuS5evVq2rZtm6QknjRpEuF0XLcF9FfXruA7URoAAAxbSURBVF2l8Y2jtDZt2kR79uyRjljCaSaJNv12Ct92HGGHGMlTOe0oYyoDmx9MBbKyssRvfvMbVUpy7SXpTwEDQ2xkRf9i+qVGia+1NOSJvFEGyjJrC4jWenQUH/2EuqGf8IGiP1GmoR21yYnrSo5gicmpV4SGcktKSujAgQPS27ioqEia5sBRnBNvYyind+/e3aqsx7L33XffbXldIJl88MEH9Nprr0nKZiy1jx492pEpEupSUVFBe/fupQULFkg9CZssJ4/R0jCcXBlVKTExMbmym66tFHQtCJgaRD8Q8D+Na1jtgW2MFUQFIjp9+rRkDAmvlKmpqZLeaNy4cYana9e2Uv2vaHLEilheXp5E1v3797esTtAbHT16VJpm4zTc6BeEPJVT3wKOqUSAiUmJSAL8lokperkdb+1QKESHDx+WJAk8LCCq2267jYYMGUJpaWmS7qN3796qdDOysr26uprOnj0rPYTQlSDgwR85ciQNHTrUsgdfbzdAFwX9Gz7QR33yySeSwhlkfdNNN7UapapRPiMvGEs2NTXRyZMnCdb2MGyVsYVkOGzYMBo8ePA1LwHlQ6W3LcmcTokhS0wJMBpiEVOsaoNcQCyNjY20b98+KQrIBQ9rZwGk1rNnT2mbBKQiPNhqSa2zvO28L5MLpBtIU7Auh/9wkEtnYdSoUdKCA+JhmggbJVjbd0Zqyoeqs3L4fnsElBgyMbXHyHVX1BKT6yqeJBVSPlRJ0mxTm6nEkO2YTIXXmsz69u0rTSusyZ1zNYIAptQczEeAicl8TE3PEYdb1tfXm54vZ2gcAWyngRElB3MRYGIyF0/OjRFgBExAgInJBBCtzgKmAMXFxVYXw/nrQACLDfCrxMFcBJiYzMXTktxk+yTWZ1gCr6FMsQKKVUwO5iLAxGQunpblhuV86DM4uAsBmGXAZoyDuQgwMZmLp2W5wRUtpg0c3IUAbMdg78XBXASYmMzF07LcMF2QrbMtK4Qz1oQAptbbt293nTW8pka4NDITk0s7RlktWGLv2rVLeZl/O4gAtgSxqYA1HcCW39bgakmusI7FPi5ZGW5JIZypagSwqRkhPz9fdRqOGBsBtvyOjUtCXMXbGd4FOLgDAbhhwaZeDuYjwBKT+ZhaliOc2kPPBF9EHJxFAJuFb7zxRvbMalI3sMRkEpBOZAO3I/L0wYnyucw2BOBmBT6ZOFiDACu/rcHVklzhRxurc/AtnRCh8Tjt3rqJXpk+np7bHetQyCtUt/9Vmp7ahbp0SaV7nttKxxsjCdE0HEklH7qQEBVOsEoyMSVYh8FZXHl5uftrHTlGb/zjQlofeJEKNlyIUd8INVa+QztpMv0+LKg5vIV+cnYRZf92D12OEdtNlzCNg38nuDfmYA0CTEzW4GpZrjgtBNM5129PSRlCM99+i36/aC7lxEIjcpqCl0bQo1k+wiBM8f1vmjX9H4je3EXBy+6WmuB8D9M4Xh2N1bHmXGNiMgdH23LBEUY4IinhV+dSbqPs7H4SKV0F7wqdrT5Ng+flUVZ3dw9LvBgeeOAB2/o8GQty9whIxh5R0ebc3FxveRuALuqNf6KiEzNo07ws6qYCA6eiyPo9PhHF2h5gYrIWX0tyHzNmjJSv/JBYUogtmUbo8u75lHrDYLp31ou04aP36aMT7tYw4UBLHFnFwVoEmJisxdey3GFtjIcksUMKdR+3lMLiWwoHN5Cf1tFD2fNp6+dXXNks2JBBv4TTUjhYiwATk7X4WpY7zpPDQ+KNjb3fJ1/mo/Tivy6hnLp99HHInVITVuKef/55VnpbNqrbMmZiasMiob5hRQgPiZc8W6YM/DH9LOdvXNkPsrSEFwIH6xFgYrIeY8tKgE3TuXPn6MMPP7SsDFszbgxT6LM76UeDu9tarJrC/H4/LVmyhKUlNWCZEIeJyQQQncxi8eLFNHfuXPfbNSlAiny+lWaljqfn1u+nOpgtRT6n3S+tprPzf0E5N39fEdvZn9ijiJCTE9Miy9nKebV0YUMgwl5HDlYhUFBQINavX29V9jrzPSfK/JkCfd/6ySkVoeaW7BqOiNL8jNZ7vvxiEQiGhXxbZ6GmJ7tw4YIYNWqUCIVCpufNGbYhoOQI9i7ggTcOtkhMmDCBNm7c2Olx1h5orq1NwBQOp6CwRwdrYWfvAtbi60jusAaH/gMPkeu3qjiCkL5CZTczs2bN0pcBp9KNAOuYdEPnroTQfwwaNIiWL1/uroolaG1qa2tp4cKFtGzZMlZ4O9CHPJVzAHSrioS0BFcckJ5YUasfZeA4Z84cgmkAVj45WI+AcirHxGQ95raWgDc9Tu6Fo3xIUBy0I7B06VKqr6+XpCXtqTmFHgSUxMRTOT0oujgNnMnBX9O0adMIJMVBGwKrVq2iU6dO0QsvvKAtIcc2FQEmJlPhdEdm2OSLVSR8WBmuvk9gqAqXJosWLepEr9RIB165h/CWb/e55zl6Y/dxalRfLMeMgQATUwxQvHAJm3zvu+8+SVfC5NR5j4KUYKi6detWFQdYdqPMZ8voUlkh+SiT/GXnpEMJREMVBbIO0qx7H6Jntp4md7u76xwTJ2MwMTmJvsVlQ2LC0eJQ5DI5dQy2NlJS5pNGg29p8SDVbQjlzfoZ5dBRemP7AfpCGZV/q0aAiUk1VIkZkckpfr/pJ6WvKLhjJ9XlTKC7Bl7fUkiEGmtP0BHyUc7YodQ3ftF8Nw4CTExxwPHKLZmcYErACvG2XoU+Sf30rS2d9O2vp6kicIDS7x9OaXiKInV0YGsJPT1tHQ32r6KVPx0U5TZYkZZ/do5A224V674p98FYVxLnHA+BQCAg7fuqrKyMF83z95qamsTKlStFbm6uqKmp0dXe5lCpyIneByh9f1AUBy/qyi/ZEyk5giWmzrnbMzFgLAjL8CeeeEJS8nqmYRoagn2F0LkdOnSINm/erELRHSvzb+hE+bu0k56kQPg7ErIHzuwKKnj2X2h3nTs9cMZqiVuvMTG5tWcsqhdMCbDyhGlMsu2tg490bHaGa9y1a9d2YhIQrwMaqTZ0kignizL6XkdE8MD5c1rw6xnk27OYpv1zuevPxovXOjfcY2JyQy/YXAcYYUJa6NGjh7SFJfEPNYgPIFYkYc0NSXHNmjUEUwpD4fJh2vFmlH5JyiyFuv6wF3Ulorqz9fTfhgrgxExMSToG4Jp3/vz50oOKBxYPLqY5XgtYdZOP8t67dy+ZcexS5Gw1HazLpIdG9CfIS1dDPR16fw99xityMiDG/tuhdFMqtuwok8tQj4CsDIZDNCjI8TvRA5TacKCHNpmq7G+uFoGZGYJ8haLs0lW3ds3hj8U6f47k9M6Xv05UNbjN3Z37e1PJEba4llQW6n6YkrOG8NKIhxmrVeXl5QkJAjxOYsUNY85skv0uWCzS263EtXjozPaL0m1BEWZO0jVulBzB3gWMCZyeTI3pj3z6SkFBAY0YMcKAotgeiGCftW3bNnr66adp5cqVNHXqVIIDPQ6JgYDSuwATU2L0myO1BEFt375dOr8ORpqTJk1y3cMeXUcotZmQHBkqhgtlYjIMYfJlIEsjMDHA3rspU6bQyJEjHSMprCLCtUt0fWACAIU+h8REgIkpMfvNFbXGsntFRQVhdWvBggU0e/ZsySZo9OjRknM6q4gBq4VVVVVSuZiupaamSp4lx40bp9NA0hVwciWiEGBiigKDvxpDAJLL4cOH6YMPPiAcnw2igkQF4sjIyKCuXbtqIg4QX01NjXSI5xdffEH79u2TppGoZV5eniSlDR06VFOexlrIqe1CgInJLqSTrByZVI4ePUrhcJjOnDlDOFYbOiqE3NzcDl39yop2xAO59ezZkyCF9e3bl/r3789ElARjiYkpCTrZjU0ESXUUevfu7Zi+qqM68XV7EWBishdvLo0RYARUIKAkJt6SogI0jsIIMAL2IsDEZC/eXBojwAioQICJSQVIHIURYATsRYCJyV68uTRGgBFQgQATkwqQOAojwAjYiwATk714c2mMACOgAgEmJhUgcRRGgBGwFwEmJnvx5tIYAUZABQJMTCpA4iiMACNgLwJMTPbizaUxAoyACgSYmFSAxFEYAUbAXgSYmOzFm0tjBBgBFQgwMakAiaMwAoyAvQi0HYtlcbnYPcyBEWAEGAE1CNhCTELgNB0OjAAjwAioQ4Cncupw4liMACNgIwJMTDaCzUUxAoyAOgSYmNThxLEYAUbARgT+P9Z+4pS1sdvsAAAAAElFTkSuQmCC"></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>
<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,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"></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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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 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>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>
<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>
<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,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" 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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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>
<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 src="data:image/png;base64,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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>
<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>
<br><hr><br>