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</div><h2>HL Paper 1</h2><div class="specification">
<p class="p1"><span class="s1">\(A\) and \(B\) </span>are independent events such that \({\text{P}}(A) = {\text{P}}(B) = p,{\text{ }}p \ne 0\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \({\text{P}}(A \cup B) = 2p - {p^2}\).</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"><span class="s1">Find \({\text{P}}(A|A \cup B)\) </span>in simplest form.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\)</p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A){\text{P}}(B)\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = p + p - {p^2}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = 2p - {p^2}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(A|A \cup B) = \frac{{{\text{P}}\left( {A \cap (A \cup B)} \right)}}{{{\text{P}}(A \cup B)}}\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2"> </p>
<p class="p1"><span class="s1"><strong>Note: <span class="Apple-converted-space"> </span></strong></span>Allow \({\text{P}}(A \cap A \cup B)\) if seen on the numerator.</p>
<p class="p3"> </p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{{{\text{P}}(A)}}{{{\text{P}}(A \cup B)}}\) </span><span class="s1"><strong><em>(A1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{p}{{2p - {p^2}}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{{2 - p}}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p4"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) posed few problems. Part (b) was possibly a good discriminator for the 4/5 candidates. Some were aware of an alternative (useful) form for the conditional probability, but were unable to interpret \(P\left( {A \cap (A \cup B)} \right)\). Large numbers of fully correct answers were seen.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Part (a) posed few problems. Part (b) was possibly a good discriminator for the 4/5 candidates. Some were aware of an alternative (useful) form for the conditional probability, but were unable to interpret \(P\left( {A \cap (A \cup B)} \right)\). Large numbers of fully correct answers were seen.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The ten numbers \({x_1},{\text{ }}{x_2},{\text{ }} \ldots ,{\text{ }}{x_{10}}\) have a mean of 10 and a standard deviation of 3.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of \(\sum\limits_{i = 1}^{10} {{{({x_i} - 12)}^2}} \).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let \({y_i} = {x_i} - 12\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar x = 10 \Rightarrow \bar y = - 2\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\sigma _x} = {\sigma _y} = 3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{\sum\limits_{i = 1}^{10} {y_i^2} }}{{10}} - {{\bar y}^2} = 9\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{i = 1}^{10} {y_i^2} = 10(9 + 4) = 130\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{i = 1}^{10} {{{({x_i} - 12)}^2} = \sum\limits_{i = 1}^{10} {x_i^2 - 24\sum\limits_{i = 1}^{10} {{x_i} + 144\sum\limits_{i = 1}^{10} 1 } } } \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\bar x = 10 \Rightarrow \sum\limits_{i = 1}^{10} {{x_i} = 100} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\sigma _x} = 3,{\text{ }}\frac{{\sum\limits_{i = 1}^{10} {x_i^2} }}{{10}} - {{\bar x}^2} = 9\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \sum\limits_{i = 1}^{10} {x_i^2} = 10(9 + 100)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\sum\limits_{i = 1}^{10} {{{({x_i} - 12)}^2} = 1090 - 2400 + 1440 = 130} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Very few candidates answered this question well, but among those a variety of nice approaches were seen. Most candidates though revealed an inability to deal with sigma expressions, especially \(\sum\limits_{i = 1}^{i = 10} {144} \). Some tried to use expectation algebra but could not then relate those results to sigma expressions (often the factor 10 was forgotten). In a few cases candidates attempted to show the result using particular examples.</span></p>
</div>
<br><hr><br><div class="specification">
<p>The continuous random variable <em>X</em> has a probability density function given by</p>
<p style="padding-left: 120px;">\(f(x) = \left\{ {\begin{array}{*{20}{l}}<br> {k\sin \left( {\frac{{\pi x}}{6}} \right),}&{0 \leqslant x \leqslant \,6} \\ <br> {0,}&{{\text{otherwise}}} <br>\end{array}} \right.\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Find the value of \(k\).</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>By considering the graph of <em>f </em>write down the mean of \(X\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By considering the graph of <em>f </em>write down the median of \(X\);</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>By considering the graph of <em>f </em>write down the mode of \(X\).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that \(P(0 \leqslant X \leqslant 2) = \frac{1}{4}\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Hence state the interquartile range of \(X\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate \(P(X \leqslant 4|X \geqslant 3)\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>attempt to equate integral to 1 (may appear later) <strong><em>M1</em></strong></p>
<p>\(k\int\limits_0^6 {\sin \left( {\frac{{\pi x}}{6}} \right){\text{d}}x = 1} \)</p>
<p>correct integral <strong><em>A1</em></strong></p>
<p>\(k\left[ { - \frac{6}{\pi }\cos \left( {\frac{{\pi x}}{6}} \right)} \right]_0^6 = 1\)</p>
<p>substituting limits <strong><em>M1</em></strong></p>
<p>\( - \frac{6}{\pi }( - 1 - 1) = \frac{1}{k}\)</p>
<p>\(k = \frac{\pi }{{12}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mean \( = 3\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A0A0 </em></strong>for three equal answers in \((0,{\text{ }}6)\).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>median \( = 3\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A0A0 </em></strong>for three equal answers in \((0,{\text{ }}6)\).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>mode \( = 3\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Award <strong><em>A1A0A0 </em></strong>for three equal answers in \((0,{\text{ }}6)\).</p>
<p> </p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(\frac{\pi }{{12}}\int\limits_0^2 {\sin } \left( {\frac{{\pi x}}{6}} \right){\text{d}}x\) <strong><em>M1</em></strong></p>
<p>\( = \frac{\pi }{{12}}\left[ { - \frac{6}{\pi }\cos \left( {\frac{{\pi x}}{6}} \right)} \right]_0^2\) <strong><em>A1</em></strong></p>
<p> </p>
<p><strong>Note:</strong> Accept without the \(\frac{\pi }{{12}}\) at this stage if it is added later.</p>
<p> </p>
<p>\(\frac{\pi }{{12}}\left[ { - \frac{6}{\pi }\left( {\cos \frac{\pi }{3} - 1} \right)} \right]\) <strong><em>M1</em></strong></p>
<p>\( = \frac{1}{4}\) <strong><em>AG</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>from (c)(i) \({Q_1} = 2\) <strong><em>(A1)</em></strong></p>
<p>as the graph is symmetrical about the middle value \(x = 3 \Rightarrow {Q_3} = 4\) <strong><em>(A1)</em></strong></p>
<p>so interquartile range is</p>
<p>\(4 - 2\)</p>
<p>\( = 2\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(P(X \leqslant 4|X \geqslant 3) = \frac{{P(3 \leqslant X \leqslant 4)}}{{P(X \geqslant 3)}}\)</p>
<p>\( = \frac{{\frac{1}{4}}}{{\frac{1}{2}}}\) <strong><em>(M1)</em></strong></p>
<p>\( = \frac{1}{2}\) <strong><em>A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="question">
<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 discrete random variable <em>X </em>has probability distribution:</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-16_om_05.33.04.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the value of <em>a</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find \({\text{E}}(X)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Find \({\text{Var}}(X)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\frac{1}{6} + \frac{1}{2} + \frac{3}{{10}} + a = 1 \Rightarrow a = \frac{1}{{30}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({\text{E}}(X) = \frac{1}{2} + 2 \times \frac{3}{{10}} + 3 \times \frac{1}{{30}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><br></em></strong>\(= \frac{6}{5}\) <em><strong>A1</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note:</strong> Do not award <strong><em>FT </em></strong>marks if <em>a </em>is outside [0, 1].</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \({\text{E}}({X^2}) = \frac{1}{2} + {2^2} \times \frac{3}{{10}} + {3^2} \times \frac{1}{{30}} = 2\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">attempt to apply \({\text{Var}}(X) = {\text{E}}({X^2}) - {\left( {{\text{E}}(X)} \right)^2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( { = 2 - \frac{{36}}{{25}}} \right) = \frac{{14}}{{25}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This was very well answered and many fully correct solutions were seen. A small number of candidates made arithmetic mistakes in part a) and thus lost one or two accuracy marks. A few also seemed unaware of the formula \({\text{Var}}(X) = {\text{E}}({X^2}) - {\text{E}}{(X)^2}\) and resorted to seeking an alternative, sometimes even attempting to apply a clearly incorrect \({\text{Var}}(X) = \sum {{{({x_i} - \mu )}^2}} \).</span></p>
</div>
<br><hr><br><div class="specification">
<p>The discrete random variable <em>X</em> has the following probability distribution, where<em> p</em> is a constant.</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>Find the value of <em>p</em>.</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 <em>μ</em>, the expected value of <em>X</em>.</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>Find P(<em>X</em> > <em>μ</em>).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>equating sum of probabilities to 1 (<em>p</em> + 0.5 − <em>p</em> + 0.25 + 0.125 + <em>p</em><sup>3</sup> = 1) <em><strong>M1</strong></em></p>
<p><em>p</em><sup>3</sup> = 0.125 = \(\frac{1}{8}\)</p>
<p><em>p</em>= 0.5 <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>μ</em> = 0 × 0.5 + 1 × 0 + 2 × 0.25 + 3 × 0.125 + 4 × 0.125 <em><strong> M1</strong></em></p>
<p>= 1.375 \(\left( { = \frac{{11}}{8}} \right)\) <em><strong>A1</strong></em></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>P(<em>X</em> > <em>μ</em>) = P(<em>X</em> = 2) + P(<em>X</em> = 3) + P(<em>X</em> = 4) <em><strong>(M1)</strong></em></p>
<p>= 0.5 <em><strong>A1</strong></em></p>
<p><strong>Note:</strong> Do not award follow through <em><strong>A</strong></em> marks in (b)(i) from an incorrect value of <em>p</em>.</p>
<p><strong>Note:</strong> Award <em><strong>M</strong> </em>marks in both (b)(i) and (b)(ii) provided no negative probabilities, and provided a numerical value for <em>μ</em> has been found.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">On Saturday, Alfred and Beatrice play 6 different games against each other. In each game, one of the two wins. The probability that Alfred wins any one of these games is \(\frac{2}{3}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Show that the probability that Alfred wins exactly 4 of the games is \(\frac{{80}}{{243}}\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Explain why the total number of possible outcomes for the results of the 6 games is 64.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) By expanding \({(1 + x)^6}\) and choosing a suitable value for <em>x</em>, prove</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[64 = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) State the meaning of this equality in the context of the 6 games played.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The following day Alfred and Beatrice play the 6 games again. Assume that the probability that Alfred wins any one of these games is still \(\frac{2}{3}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for the probability Alfred wins 4 games on the first day and 2 on the second day. Give your answer in the form \({\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> r <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^s}{\left( {\frac{1}{3}} \right)^t}\) where the values of <em>r</em>, <em>s</em> and <em>t</em> are to be found.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) Using your answer to (c) (i) and 6 similar expressions write down the probability that Alfred wins a total of 6 games over the two days as the sum of 7 probabilities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Hence prove that \(\left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 6 <br>\end{array}} \right) = {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)^2}\).</span></p>
<div class="marks">[9]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Alfred and Beatrice play <em>n</em> games. Let <em>A</em> denote the number of games Alfred wins. The expected value of <em>A</em> can be written as \({\text{E}}(A) = \sum\limits_{r = 0}^n {r\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} \frac{{{a^r}}}{{{b^n}}}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find the values of <em>a</em> and <em>b</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) By differentiating the expansion of \({(1 + x)^n}\), prove that the expected number of games Alfred wins is \(\frac{{2n}}{3}\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(B\left( {6,\frac{2}{3}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(p(4) = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right){\left( {\frac{2}{3}} \right)^4}{\left( {\frac{1}{3}} \right)^2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right) = 15\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 15 \times \frac{{{2^4}}}{{{3^6}}} = \frac{{80}}{{243}}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) 2 outcomes for each of the 6 games or \({2^6} = 64\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({(1 + x)^6} = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)x + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right){x^2} + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right){x^3} + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right){x^4} + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right){x^5} + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right){x^6}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept \(^n{C_r}\) notation or \(1 + 6x + 15{x^2} + 20{x^3} + 15{x^4} + 6{x^5} + {x^6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica; min-height: 30.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">setting <em>x</em> = 1 in both sides of the expression <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Do not award <strong><em>R1</em></strong> if the right hand side is not in the correct form.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">\(64 = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right) + \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)\)</span> <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) the total number of outcomes = number of ways Alfred can win no games, plus the number of ways he can win one game <em>etc.</em> <strong><em>R1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Let \({\text{P}}(x,{\text{ }}y)\) be the probability that Alfred wins <em>x</em> games on the first day and <em>y</em> on the second.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P(4, 2)}} = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right) \times {\left( {\frac{2}{3}} \right)^4} \times {\left( {\frac{1}{3}} \right)^2} \times \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right) \times {\left( {\frac{2}{3}} \right)^2} \times {\left( {\frac{1}{3}} \right)^4}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^6}\) or </span><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^6}\)</span> <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>r</em> = 2 or 4, <em>s</em> = <em>t</em> = 6</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) P(Total = 6) =</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(0, 6) + P(1, 5) + P(2, 4) + P(3, 3) + P(4, 2) + P(5, 1) + P(6, 0) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^6} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^6} + ... + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)^2}{\left( {\frac{2}{3}} \right)^6}{\left( {\frac{1}{3}} \right)^6}\) <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{2^6}}}{{{3^{12}}}}\left( {{{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)}^2}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept any valid sum of 7 probabilities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) use of \(\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> i <br>\end{array}} \right) = \left( {\begin{array}{*{20}{l}}<br> 6 \\ <br> {6 - i} <br>\end{array}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(can be used either here or in (c)(ii))</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(wins 6 out of 12) \( = \left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 6 <br>\end{array}} \right) \times {\left( {\frac{2}{3}} \right)^6} \times {\left( {\frac{1}{3}} \right)^6} = \frac{{{2^6}}}{{{3^{12}}}}\left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 6 <br>\end{array}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{{2^6}}}{{{3^{12}}}}\left( {{{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right)}^2} + {{\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)}^2}} \right) = \frac{{{2^6}}}{{{3^{12}}}}\left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 6 <br>\end{array}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore \({\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 0 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 1 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 2 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 4 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 5 <br>\end{array}} \right)^2} + {\left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 6 <br>\end{array}} \right)^2} = \left( {\begin{array}{*{20}{c}}<br> {12} \\ <br> 6 <br>\end{array}} \right)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) \({\text{E}}(A) = \sum\limits_{r = 0}^n {r\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} {\left( {\frac{2}{3}} \right)^r}{\left( {\frac{1}{3}} \right)^{n - r}} = \sum\limits_{r = 0}^n {r\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} \frac{{{2^r}}}{{{3^n}}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(<em>a</em> = 2, <em>b</em> = 3) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> <strong><em>M0A0</em></strong> for <em>a</em> = 2, <em>b</em> = 3 without any method.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica; min-height: 29.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \(n{(1 + x)^{n - 1}} = \sum\limits_{r = 1}^n {\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} r{x^{r - 1}}\) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(sigma notation not necessary)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(if sigma notation used also allow lower limit to be <em>r</em> = 0)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">let <em>x</em> = 2 <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(n{3^{n - 1}} = \sum\limits_{r = 1}^n {\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} r{2^{r - 1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">multiply by 2 and divide by \({3^n}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{2n}}{3} = \sum\limits_{r = 1}^n {\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} r\frac{{{2^r}}}{{{3^n}}}\left( { = \sum\limits_{r = 0}^n {\left( {\begin{array}{*{20}{c}}<br> n \\ <br> r <br>\end{array}} \right)} \frac{{{2^r}}}{{{3^n}}}} \right)\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question linked the binomial distribution with binomial expansion and coefficients and was generally well done.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(a) Candidates need to be aware how to work out binomial coefficients without a calculator</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question linked the binomial distribution with binomial expansion and coefficients and was generally well done.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(b) (ii) A surprising number of candidates chose to work out the values of all the binomial coefficients (or use Pascal’s triangle) to make a total of 64 rather than simply putting 1 into the left hand side of the expression.<br></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question linked the binomial distribution with binomial expansion and coefficients and was generally well done.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">This question linked the binomial distribution with binomial expansion and coefficients and was generally well done.</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">(d) This was poorly done. Candidates were not able to manipulate expressions given using sigma notation.<br></span></p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Consider the following functions:</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \frac{{2{x^2} + 3}}{{75}},{\text{ }}x \geqslant 0\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\[g(x) = \frac{{\left| {3x - 4} \right|}}{{10}},{\text{ }}x \in \mathbb{R}{\text{ }}.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">State the range of <em>f </em>and of <em>g </em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find an expression for the composite function \(f \circ g(x)\) in the form \(\frac{{a{x^2} + bx + c}}{{3750}}\), where \(a,{\text{ }}b{\text{ and }}c \in \mathbb{Z}\) .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) Find an expression for the inverse function \({f^{ - 1}}(x)\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) State the domain and range of \({f^{ - 1}}\)<span style="font: 7.0px Helvetica;"> </span>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="line-height: normal; font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;">The domains of <em>f</em> and <em>g</em> are now restricted to {0, 1, 2, 3, 4} .</span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">By considering the values of <em>f </em>and <em>g </em>on this new domain, determine which of <em>f </em>and <em>g </em>could be used to find a probability distribution for a discrete random variable <em>X </em>, stating your reasons clearly.</span></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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Using this probability distribution, calculate the mean of <em>X </em>.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f(x) \geqslant \frac{1}{{25}}\) <strong> <em>A1 </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(g(x) \in \mathbb{R},{\text{ }}g(x) \geqslant 0\) <strong> <em>A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f \circ g(x) = \frac{{2{{\left( {\frac{{3x - 4}}{{10}}} \right)}^2} + 3}}{{75}}\) <strong> <em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\frac{{2(9{x^2} - 24x + 16)}}{{100}} + 3}}{{75}}\) <strong> <em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{9{x^2} - 24x + 166}}{{3750}}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[4 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2{x^2} + 3}}{{75}}\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({x^2} = \frac{{75y - 3}}{2}\) <strong> <em>M1</em></strong></span></p>
<p>\(x = \sqrt {\frac{{75y - 3}}{2}} \) <strong> <em>(A1)</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = \sqrt {\frac{{75x - 3}}{2}} \) <strong> <em>A1</em></strong></span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept ± in line 3 for the <strong><em>(A1) </em></strong>but not in line 4 for the <strong><em>A1</em></strong>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award the <strong><em>A1 </em></strong>only if written in the form \({f^{ - 1}}(x) = \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \frac{{2{x^2} + 3}}{{75}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = \frac{{2{y^2} + 3}}{{75}}\) <strong><em>M1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(y = \sqrt {\frac{{75x - 3}}{2}} \) <strong><em>(A1)</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow {f^{ - 1}}(x) = \sqrt {\frac{{75x - 3}}{2}} \) <strong><em>A1</em></strong></span> <span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Accept ± in line 3 for the <strong><em>(A1) </em></strong>but not in line 4 for the <strong><em>A1</em></strong>.</span><span style="font-family: 'Helvetica Neue', Arial, 'Lucida Grande', 'Lucida Sans Unicode', sans-serif; font-size: 14px; line-height: 20px;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award the <strong><em>A1 </em></strong>only if written in the form \({f^{ - 1}}(x) = \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) domain: \(x \geqslant \frac{1}{{25}}\) ; range: \({f^{ - 1}}(x) \geqslant 0\) <strong><em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">probabilities from \(f(x)\) :</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><img src="data:image/png;base64,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" alt> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for one error, <strong><em>A0 </em></strong>otherwise.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">probabilities from \(g(x)\) :</span></p>
<p><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A2<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <strong><em>A1 </em></strong>for one error, <strong><em>A0 </em></strong>otherwise. </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">only in the case of \(f(x)\) does \(\sum {P(X = x) = 1} \) , hence only \(f(x)\) can be used as a probability mass function <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[6 marks]</span><br></em></strong></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\(E(x) = \sum {x \cdot {\text{P}}(X = x)} \) <strong> <em>M1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{5}{{75}} + \frac{{22}}{{75}} + \frac{{63}}{{75}} + \frac{{140}}{{75}} = \frac{{230}}{{75}}\left( { = \frac{{46}}{{15}}} \right)\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">In (a), the ranges were often given incorrectly, particularly the range of <em>g </em>where the modulus signs appeared to cause difficulty. In (b), it was disappointing to see so many candidates making algebraic errors in attempting to determine the expression for \(f \circ g(x)\). Many candidates were unable to solve (d) correctly with arithmetic errors and incorrect reasoning often seen. Since the solution to (e) depended upon a correct choice of function in (d), few correct solutions were seen with some candidates even attempting to use integration, inappropriately, to find the mean of <em>X</em>.</span></p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-family: times new roman,times; font-size: medium;">In a population of rabbits, \(1\%\) are known to have a particular disease. A test is developed for the disease that gives a positive result for a rabbit that <strong>does</strong> have the disease in \(99\%\) of cases. It is also known that the test gives a positive result for a rabbit that <strong>does not</strong> have the disease in \(0.1\%\) of cases. A rabbit is chosen at random from the population.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the probability that the rabbit tests positive for the disease.</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 style="font-family: times new roman,times; font-size: medium;">Given that the rabbit tests positive for the disease, show that the probability that the rabbit does not have the disease is less than 10 %.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><em>R</em> is ‘rabbit with the disease’</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>P</em> is ‘rabbit testing positive for the disease’</span></p>
<p><span style="font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(P) = P(R \cap P) + P(R' \cap P)\)<br></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.01 \times 0.99 + 0.99 \times 0.001\) <em><strong>M1</strong></em><br></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.01089( = 0.0109)\) <em><strong>A1</strong></em><br></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: </strong>Award <em><strong>M1</strong></em> for a correct tree diagram with correct probability values shown.<em><strong><br></strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: times new roman,times;"><span style="font-size: medium;"><em><strong>[2 marks]</strong></em></span><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;"><em>R</em> is ‘rabbit with the disease’</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em>P</em> is ‘rabbit testing positive for the disease’</span></p>
<p><span style="font-family: times new roman,times;"><img src="data:image/png;base64,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" alt></span></p>
<p><span style="font-family: times new roman,times;"> </span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\(P(R'|P) = \frac{{0.001 \times 0.99}}{{0.001 \times 0.99 + 0.01 \times 0.99}}\left( { = \frac{{0.00099}}{{0.01089}}} \right)\) <em><strong>M1A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{0.00099}}{{0.01089}} < \frac{{0.001}}{{0.01}} = 10\% \) (or other valid argument) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>R1</strong></em></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[3 marks]</strong></em><br></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was a mixed performance in this question with some candidates showing good understanding of probability and scoring well and many others showing no understanding of conditional probability and difficulties in working with decimals. Very few candidates were able to provide a valid argument to justify their answer to part (b).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">There was a mixed performance in this question with some candidates showing good understanding of probability and scoring well and many others showing no understanding of conditional probability and difficulties in working with decimals. Very few candidates were able to provide a valid argument to justify their answer to part (b).</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let <em>A</em> and <em>B</em> be events such that \({\text{P}}(A) = 0.6,{\text{ P}}(A \cup B) = 0.8{\text{ and P}}(A|B) = 0.6\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find P(<em>B</em>) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using \({\text{P}}(A|B) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.6{\text{P}}(B) = {\text{P}}(A \cap B)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\) to obtain \(0.8 = 0.6 + {\text{P}}(B) - {\text{P}}(A \cap B)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Substituting \(0.6{\text{P}}(B) = {\text{P}}(A \cap B)\) into above equation <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">As \({\text{P}}(A|B) = {\text{P}}(A)\) then <em>A</em> and <em>B</em> are independent events <strong><em>M1R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Using \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A) \times {\text{P}}(B)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">to obtain \(0.8 = 0.6 + {\text{P}}(B) - 0.6 \times {\text{P}}(B)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>THEN</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.8 = 0.6 + 0.4{\text{P}}(B)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B) = 0.5\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well done, with a few candidates spotting an opportunity to use results for the <em>independent events</em> A and B.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A bag contains three balls numbered 1, 2 and 3 respectively. Bill selects one of these balls at random and he notes the number on the selected ball. He then tosses that number of fair coins.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Calculate the probability that no head is obtained.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that no head is obtained, find the probability that he tossed two coins.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(no heads from <em>n</em> coins tossed) = \({0.5^n}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(no head) = \(\frac{1}{3} \times \frac{1}{2} + \frac{1}{3} \times \frac{1}{4} + \frac{1}{3} \times \frac{1}{8}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= \(\frac{7}{{24}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P(2 | no heads)}} = \frac{{{\text{P(2 coins and no heads)}}}}{{{\text{P(no heads)}}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\frac{1}{{12}}}}{{\frac{7}{{24}}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{2}{7}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Events \(A\) and \(B\) are such that \({\text{P}}(A) = 0.2\) and \({\text{P}}(B) = 0.5\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Determine the value of \({\text{P}}(A \cup B)\) when</p>
<p class="p1">(i) <span class="Apple-converted-space"> </span>\(A\) and \(B\) are mutually exclusive;</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>\(A\) and \(B\) are independent.</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 class="p1">Determine the range of possible values of \({\text{P}}\left( {A|B} \right)\).</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>use of \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({\text{P}}(A \cup B) = 0.2 + 0.5\)</p>
<p class="p1">\( = 0.7\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span><span class="s1">use of </span>\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A){\text{P}}(B)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1">\({\text{P}}(A \cup B) = 0.2 + 0.5 - 0.1\)</p>
<p class="p1">\( = 0.6\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{P}}\left( {A|B} \right) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}}\)</p>
<p class="p1">\({\text{P}}\left( {A|B} \right)\) is a maximum when \({\text{P}}(A \cap B) = {\text{P}}(A)\)</p>
<p class="p1">\({\text{P}}\left( {A|B} \right)\) is a minimum when \({\text{P}}(A \cap B) = 0\)</p>
<p class="p1">\(0 \le {\text{P}}\left( {A|B} \right) \le 0.4\) <span class="Apple-converted-space"> </span><strong><em>A1A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span><em>A1 </em></strong>for each endpoint and <strong><em>A1 </em></strong>for the correct inequalities.</p>
<p class="p1"><em><strong>[3 marks]</strong></em></p>
<p class="p1"><em><strong>Total [7 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This part was generally well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Disappointingly, many candidates did not seem to understand the meaning of the word ‘range’ in this context.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">Two events \(A\) and \(B\) <span class="s1">are such that \({\text{P}}(A \cap B') = 0.2\) and \({\text{P}}(A \cup B) = 0.9\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">On the Venn diagram shade the region \(A' \cap B'\).</p>
<p class="p1"><img src="images/Schermafbeelding_2017-01-31_om_07.46.49.png" alt="M16/5/MATHL/HP1/ENG/TZ1/04"></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 class="p1">Find \({\text{P}}(A'|B')\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space"><img src="images/Schermafbeelding_2017-01-31_om_07.50.22.png" alt="M16/5/MATHL/HP1/ENG/TZ1/04/M"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(P(A'|B') = \frac{{P(A' \cap B')}}{{P(B')}}\) </span><strong><em>(M1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(P(B') = 0.1 + 0.2 = 0.3\) </span><strong><em>(A1)</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\(P(A' \cap B') = 0.1\) </span><strong><em>(A1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(P(A'|B') = \frac{{0.1}}{{0.3}} = \frac{1}{3}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Part (a) was well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">In part (b) some candidates were unable to write down the conditional probability formula. Some then failed to realise that part (a) was designed to help them work out \(P(A' \cap B')\) and instead incorrectly assumed independence.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">\(A\) and \(B\) are two events such that \({\text{P}}(A) = 0.25,{\text{ P}}(B) = 0.6\) and \({\text{P}}(A \cup B) = 0.7\).</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find \({\text{P}}(A \cap B)\).</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">Determine whether events \(A\) and \(B\) are independent.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\)</p>
<p class="p1">\({\text{P}}(A \cap B) = 0.25 + 0.6 = 0.7\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1">\( = 0.15\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p2">\({\text{P}}(A){\text{P}}(B)( = 0.25 \times 0.6) = 0.15\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\( = {\text{P}}(A \cap B)\) so independent <strong><em>R1</em></strong></p>
<p class="p2"><strong><em>OR</em></strong></p>
<p class="p2">\({\text{P}}(A|B) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}} = \frac{{0.15}}{{0.6}} = 0.25\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2">\( = {\text{P}}(A)\) so independent <strong><em>R1</em></strong></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Allow follow through for incorrect answer to (a) that will result in events being dependent in (b).</p>
<p class="p1"><em><strong>[2 marks]</strong></em></p>
<p class="p1"><em><strong>Total [4 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Two unbiased tetrahedral (four-sided) dice with faces labelled 1, 2, 3, 4 are thrown and the scores recorded. Let the random variable <em>T</em> be the maximum of these two scores.</p>
<p>The probability distribution of <em>T</em> is given in the following table.</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>Find the value of <em>a</em> and the value of <em>b</em>.</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>Find the expected value of <em>T</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\(a = \frac{3}{{16}}\) and \(b = \frac{5}{{16}}\) <em><strong>(M1)A1A1</strong></em></p>
<p><em><strong>[3 marks]</strong></em></p>
<p><strong>Note:</strong> Award <em><strong>M1</strong></em> for consideration of the possible outcomes when rolling the two dice.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{E}}\left( T \right) = \frac{{1 + 6 + 15 + 28}}{{16}} = \frac{{25}}{8}\left( { = 3.125} \right)\) <em><strong>(M1)A1</strong></em></p>
<p><strong>Note:</strong> Allow follow through from part (a) even if probabilities do not add up to 1.</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A biased coin is weighted such that the probability of obtaining a head is \(\frac{4}{7}\). The coin is tossed 6 times and <em>X</em> denotes the number of heads observed. Find the value of the ratio \(\frac{{{\text{P}}(X = 3)}}{{{\text{P}}(X = 2)}}\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">recognition of \(X \sim {\text{B}}\left( {6,\frac{4}{7}} \right)\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = 3) = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right){\left( {\frac{4}{7}} \right)^3}{\left( {\frac{3}{7}} \right)^3}\left( { = 20 \times \frac{{{4^3} \times {3^3}}}{{{7^6}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = 2) = \left( {\begin{array}{*{20}{c}}<br> 6 \\ <br> 3 <br>\end{array}} \right){\left( {\frac{4}{7}} \right)^2}{\left( {\frac{3}{7}} \right)^4}\left( { = 15 \times \frac{{{4^2} \times 34}}{{{7^6}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{P}}(X = 3)}}{{{\text{P}}(X = 2)}} = \frac{{80}}{{45}}\left( { = \frac{{16}}{9}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many correct answers were seen to this and the majority of candidates recognised the need to use a Binomial distribution. A number of candidates, although finding the correct expressions for \({\text{P}}(X = 3)\) and \({\text{P}}(X = 4)\), were unable to perform the required simplification.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">In a particular city 20 % of the inhabitants have been immunized against a certain disease. The probability of infection from the disease among those immunized is \(\frac{1}{{10}}\), and among those not immunized the probability is \(\frac{3}{4}\). If a person is chosen at random and found to be infected, find the probability that this person has been immunized.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">tree diagram <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P(I|D)}} = \frac{{{\text{P(D|I)}} \times {\text{P(I)}}}}{{{\text{P(D)}}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{0.1 \times 0.2}}{{0.1 \times 0.2 + 0.8 \times 0.75}}\) <strong><em>A1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( { = \frac{{0.02}}{{0.62}}} \right) = \frac{1}{{31}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Alternative presentation of results: </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for labelled tree; </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for initial branching probabilities, 0.2 and 0.8; </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for at least the relevant second branching probabilities, 0.1 and 0.75; </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the ‘infected’ end-point probabilities, 0.02 and 0.6; </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1A1</em></strong><span style="font-family: 'times new roman', times; font-size: medium;"> for the final conditional probability calculation.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates who drew a tree diagram, the majority, usually found the correct answer.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A mathematics test is given to a class of <span class="s1">20 </span>students. One student scores <span class="s1">0</span>, but all the other students score <span class="s1">10</span>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Find the mean score for the class.</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">Write down the median score.</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">Write down the number of students who scored</p>
<p class="p1">(i) above the mean score;</p>
<p class="p1">(ii) below the median score.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">\(\bar x = \frac{{1 \times 0 + 19 \times 10}}{{20}} = 9.5\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)A1</em></strong></span></p>
<p class="p1"><span class="s1"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">median is <span class="s1">\(10\) </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="s1">\(19\) </span><strong><em>A1</em></strong></p>
<p class="p1">(ii) <span class="s1">\(1\)</span><span class="s1"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<p class="p1"><strong><em>Total [5 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well done.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Well done.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Both parts well done.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">At a nursing college, 80 % of incoming students are female. College records show that 70 % of the incoming females graduate and 90 % of the incoming males graduate. A student who graduates is selected at random. Find the probability that the student is male, giving your answer as a fraction in its lowest terms.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P }}M|G = \frac{{{\text{P}}(M \cap G)}}{{{\text{P}}(G)}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{0.2 \times 0.9}}{{0.2 \times 0.9 + 0.8 \times 0.7}}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{0.18}}{{0.74}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{9}{{37}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates answered this question successfully. Some made arithmetic errors.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The probability distribution of a discrete random variable <em>X</em> is defined by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = x) = cx(5 - x),{\text{ }}x = {\text{1, 2, 3, 4}}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Find the value of <em>c</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find <em>E</em>(<em>X</em>) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Using \(\sum {{\text{P}}(X = x) = 1} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(4c + 6c + 6c + 4c = 1\,\,\,\,\,(20c = 1)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(c = \frac{1}{{20}}\,\,\,\,\,( = 0.05)\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Using \({\text{E}}(X) = \sum {x{\text{P}}(X = x)} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = (1 \times 0.2) + (2 \times 0.3) + (3 \times 0.3) + (4 \times 0.2)\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2.5\) <strong><em>A1</em></strong> <strong><em>N1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Notes:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Only one of the first two marks can be implied.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>M1A1A1</em></strong> if the x values are averaged only if symmetry is explicitly mentioned.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well done, but a few candidates tried integration for part (b).</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A continuous random variable X has the probability density function</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {k\sin x,}&{0 \leqslant x \leqslant \frac{\pi }{2}} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>k</em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 35.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\text{E}}(X)\).</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the median of <em>X</em>.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\int_0^{\frac{\pi }{2}} {\sin x{\text{d}}x = 1} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k[ - \cos x]_0^{\frac{\pi }{2}} = 1\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em>k</em> = 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = \int_0^{\frac{\pi }{2}} {x\sin x{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">integration by parts <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\([ - x\cos x]_0^{\frac{\pi }{2}} + \int_0^{\frac{\pi }{2}} {\cos x{\text{d}}x} \) <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^M {\sin x{\text{d}}x} = \frac{1}{2}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\([ - \cos x]_0^M = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\cos M = \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(M = \frac{\pi }{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> accept \(\arccos \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;"><em>[3 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates scored maximum marks on this question. A few candidates found k = –1.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates scored maximum marks on this question. A few candidates found k = –1.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates scored maximum marks on this question. A few candidates found k = –1.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"> </p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<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;">Mobile phone batteries are produced by two machines. Machine A produces 60% of the daily output and machine B produces 40%. It is found by testing that on average 2% of batteries produced by machine A are faulty and 1% of batteries produced by machine B are faulty.</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;">(i) Draw a tree diagram clearly showing the respective probabilities.</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;">(ii) A battery is selected at random. Find the probability that it is faulty.</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;">(iii) A battery is selected at random and found to be faulty. Find the probability that it was produced by machine A.</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 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;">In a pack of seven transistors, three are found to be defective. Three transistors are selected from the pack at random without replacement. The discrete random variable <em>X </em>represents the number of defective transistors selected.</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;">(i) Find \({\text{P}}(X = 2)\).</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;">(ii) <strong>Copy </strong>and complete the following table:</span></p>
<p style="font: normal normal normal 21px/normal 'Times New Roman'; text-align: center; margin: 0px;"><br><span style="font-family: 'times new roman', times; font-size: medium;"><img src="images/Schermafbeelding_2014-09-15_om_08.18.32.png" alt></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) Determine \({\text{E}}(X)\).</span></p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i)<br><img src="images/maths_11a_markscheme.png" alt> <strong><em>A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>for a correctly labelled tree diagram and <strong><em>A1 </em></strong>for correct probabilities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{P}}(F) = 0.6 \times 0.02 + 0.4 \times 0.01\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.016\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({\text{P}}(A|F) = \frac{{{\text{P}}(A \cap F)}}{{{\text{P}}(F)}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{0.6 \times 0.02}}{{0.016}}{\text{ }}\left( { = \frac{{0.012}}{{0.016}}} \right)\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.75\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(i) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X = 2) = \frac{{^3{C_2}{ \times ^4}{C_1}}}{{^7{C_3}}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{12}}{{35}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{3}{7} \times \frac{2}{6} \times \frac{4}{5} \times 3\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{12}}{{35}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(ii) <img src="images/Schermafbeelding_2014-09-15_om_08.21.37.png" alt> <strong><em>A2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note:</strong> Award <strong><em>A1 </em></strong>if \(\frac{4}{{35}},{\text{ }}\frac{{18}}{{35}}\) or \(\frac{1}{{35}}\) is obtained.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(iii) \({\text{E}}(X) = \sum {x{\text{P}}(X = x)} \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = 0 \times \frac{4}{{35}} + 1 \times \frac{{18}}{{35}} + 2 \times \frac{{12}}{{35}} + 3 \times \frac{1}{{35}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{45}}{{35}} = \left( {\frac{9}{7}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">The faces of a fair six-sided die are numbered <span class="s1">1, 2, 2, 4, 4, 6</span>. Let \(X\) be the discrete random variable that models the score obtained when this die is rolled.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Complete the probability distribution table for \(X\).</p>
<p class="p1"><img src="images/Schermafbeelding_2017-02-28_om_11.16.45.png" alt="N16/5/MATHL/HP1/ENG/TZ0/02.a"></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">Find the expected value of \(X\).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img src="images/Schermafbeelding_2017-02-28_om_11.18.41.png" alt="N16/5/MATHL/HP1/ENG/TZ0/02.a/M"> <strong><em>A1A1</em></strong></p>
<p class="p3"> </p>
<p class="p2"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>A1 </em></strong>for each correct row.</p>
<p class="p3"> </p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\({\text{E}}(X) = 1 \times \frac{1}{6} + 2 \times \frac{1}{3} + 4 \times \frac{1}{3} + 6 \times \frac{1}{6}\) </span><strong>(<em>M1)</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\( = \frac{{19}}{6}{\text{ }}\left( { = 3\frac{1}{6}} \right)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong><span class="s2">If the probabilities in (a) are not values between 0 and 1 </span>or lead to \({\text{E}}(X) > 6\) award <strong><em>M1A0 </em></strong>to correct method using the incorrect probabilities; otherwise allow <strong><em>FT </em></strong>marks.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The continuous random variable <em>X </em>has probability density function given by</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {a{e^{ - x}},}&{0 \leqslant x \leqslant 1} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">State the mode of <em>X </em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the value of <em>a </em>.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Find E(<em>X </em>) .</span></p>
<div class="marks">[4]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">0 <strong> <em>A1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[1 mark]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^1 {f(x)dx = 1} \) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{1}{{\int_0^1 {{e^{ - x}}dx} }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{1}{{\left[ { - {e^{ - x}}} \right]_0^1}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{e}{{e - 1}}\) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note: </strong><span style="font-family: 'times new roman', times; font-size: medium;">Award first </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1 </em></strong><span style="font-family: 'times new roman', times; font-size: medium;">for correct integration of \(\int {{e^{ - x}}dx} \) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This <strong><em>A1 </em></strong>is independent of previous <strong><em>M </em></strong>mark.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = \int_0^1 {xf(x)dx\left( { = a\int_0^1 {x{e^{ - x}}dx} } \right)} \) <em><strong>M1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">attempt to integrate by parts <strong><em>M1</em></strong></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = a\left[ { - x{e^{ - x}} - {e^{ - x}}} \right]_0^1\) <em><strong>(A1)</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = a\left( {\frac{{e - 2}}{e}} \right)\)</span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{e - 2}}{{e - 1}}\) (or equivalent) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A range of answers were seen to part a), though many more could have gained the mark had they taken time to understand the shape of the function. Part b) was done well, as was part c). In c), a number of candidates integrated by parts, but found the incorrect expression \( - x{e^{ - x}} + {e^{ - x}}\).</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A range of answers were seen to part a), though many more could have gained the mark had they taken time to understand the shape of the function. Part b) was done well, as was part c). In c), a number of candidates integrated by parts, but found the incorrect expression \( - x{e^{ - x}} + {e^{ - x}}\).</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">A range of answers were seen to part a), though many more could have gained the mark had they taken time to understand the shape of the function. Part b) was done well, as was part c). In c), a number of candidates integrated by parts, but found the incorrect expression \( - x{e^{ - x}} + {e^{ - x}}\).</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="font-size: medium; font-family: times new roman,times;">Events \(A\) and<em> </em>\(B\) are such that \({\text{P}}(A) = 0.3\) and \({\text{P}}(B) = 0.4\) .</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Find the value of \({\text{P}}(A \cup B)\) when</span><br><span style="font-family: times new roman,times; font-size: medium;">(i) \(A\) and \(B\) are mutually exclusive;</span><br><span style="font-family: times new roman,times; font-size: medium;">(ii) \(A\) and \(B\) are independent.</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 style="font-family: times new roman,times; font-size: medium;">Given that \({\text{P}}(A \cup B) = 0.6\) , find \({\text{P}}(A|B)\) .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">(i) \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) = 0.7\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;">(ii) \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\) </span><em style="font-family: 'times new roman', times; font-size: medium;"><strong>(M1)</strong></em></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> \( = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A){\text{P}}(B)\) <em><strong>(M</strong></em><em><strong>1)</strong></em><br></span></p>
<p style="margin-left: 30px;"><span style="font-family: times new roman,times; font-size: medium;"> \( = 0.3 + 0.4 - 0.12 = 0.58\) <em><strong>A1</strong></em></span></p>
<p><span style="font-family: 'times new roman', times; font-size: medium;"><em style="font-family: 'times new roman', times; font-size: medium;"><strong>[4 marks]</strong></em></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">\({\text{P}}(A \cap B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cup B)\)</span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = 0.3 + 0.4 - 0.6 = 0.1\) <em><strong>A1</strong></em><br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\({\text{P}}(A|B) = \frac{{{\text{P}}(A \cap B)}}{{{\text{P}}(B)}}\) <em><strong>(M1)</strong></em><br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;">\( = \frac{{0.1}}{{0.4}} = 0.25\) <em><strong>A1</strong></em><br></span></p>
<p><span style="font-family: times new roman,times; font-size: medium;"><em><strong>[3 marks]<br></strong></em></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question and answered it well. A few misconceptions were identified (eg \({\text{P}}(A \cup B) = {\text{P}}(A){\text{P}}(B)\) ). Many candidates were unsure about the meaning of independent events.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="font-family: times new roman,times; font-size: medium;">Most candidates attempted this question and answered it well. A few misconceptions were identified (eg \({\text{P}}(A \cup B) = {\text{P}}(A){\text{P}}(B)\) ). Many candidates were unsure about the meaning of independent events.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A random variable has a probability density function given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {kx(2 - x),}&{0 \leqslant x \leqslant 2} \\ <br> {0,}&{{\text{elsewhere}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that \(k = \frac{3}{4}\) .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find \({\text{E}}(X)\) .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\int_0^2 {kx(2 - x){\text{d}}x = 1} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for LHS and <strong><em>A1</em></strong> for setting = 1 at any stage.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ {\frac{{2k}}{2}{x^2} - \frac{k}{3}{x^3}} \right]_0^2 = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\left( {4 - \frac{8}{3}} \right) = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = \frac{3}{4}\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({\text{E}}(X) = \frac{3}{4}\int_0^2 {{x^2}(2 - x){\text{d}}x} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">= 1 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept answers that indicate use of symmetry.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The integration was particularly well done in this question. A number of students treated the distribution as discrete. On the whole a) was done well once the distribution was recognized although there was a certain amount of fudging to achieve the result. A significant number of students did not initially set the integral equal to 1. Very few noted the symmetry of the distribution in b).</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">A box contains four red balls and two white balls. Darren and Marty play a game by each taking it in turn to take a ball from the box, without replacement. The first player to take a white ball is the winner.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Darren plays first, find the probability that he wins.</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 class="p1">The game is now changed so that the ball chosen is replaced after each turn.</p>
<p class="p1">Darren still plays first.</p>
<p class="p1">Show that the probability of Darren winning has not changed.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">probability that Darren wins \({\text{P}}(W) + {\text{P}}(RRW) + {\text{P}}(RRRRW)\) <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Only award <strong><em>M1 </em></strong>if three terms are seen or are implied by the following numerical equivalent.</p>
<p class="p4"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span></strong>Accept equivalent tree diagram for method mark.</p>
<p class="p4"> </p>
<p class="p1">\( = \frac{2}{6} + \frac{4}{6} \bullet \frac{3}{5} \bullet \frac{2}{4} + \frac{4}{6} \bullet \frac{3}{5} \bullet \frac{2}{4} \bullet \frac{1}{3} \bullet \frac{2}{2}\;\;\;\left( { = \frac{1}{3} + \frac{1}{5} + \frac{1}{{15}}} \right)\) <strong><em>A2</em></strong></p>
<p class="p2"> </p>
<p class="p3"><strong>Note: <span class="Apple-converted-space"> </span><em>A1 </em></strong>for two correct.</p>
<p class="p4"> </p>
<p class="p1">\( = \frac{3}{5}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>the probability that Darren wins is given by</p>
<p>\({\text{P}}(W) + {\text{P}}(RRW) + {\text{P}}(RRRRW) + \ldots \) <strong><em>(M1)</em></strong></p>
<p> </p>
<p><strong>Note: </strong>Accept equivalent tree diagram with correctly indicated path for method mark.</p>
<p> </p>
<p>\({\text{P (Darren Win)}} = \frac{1}{3} + \frac{2}{3} \bullet \frac{2}{3} \bullet \frac{1}{3} + \frac{2}{3} \bullet \frac{2}{3} \bullet \frac{2}{3} \bullet \frac{2}{3} \bullet \frac{1}{3} + \ldots \)</p>
<p>or \( = \frac{1}{3}\left( {1 + \frac{4}{9} + {{\left( {\frac{4}{9}} \right)}^2} + \ldots } \right)\) <strong><em>A1</em></strong></p>
<p>\( = \frac{1}{3}\left( {\frac{1}{{1 - \frac{4}{9}}}} \right)\) <strong><em>A1</em></strong></p>
<p>\( = \frac{3}{5}\) <strong><em>AG</em></strong></p>
<p><strong>METHOD 2</strong></p>
<p>\({\text{P (Darren wins)}} = {\text{P}}\)</p>
<p>\({\text{P}} = \frac{1}{3} + \frac{4}{9}{\text{P}}\) <strong><em>M1A2</em></strong></p>
<p>\(\frac{5}{9}{\text{P}} = \frac{1}{3}\)</p>
<p>\({\text{P}} = \frac{3}{5}\) <strong><em>AG</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<p><strong><em>Total [7 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Chloe and Selena play a game where each have four cards showing capital letters A, B, C and D.<br>Chloe lays her cards face up on the table in order A, B, C, D as shown in the following diagram.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-02-07_om_14.39.35.png" alt="N17/5/MATHL/HP1/ENG/TZ0/10"></p>
<p>Selena shuffles her cards and lays them face down on the table. She then turns them over one by one to see if her card matches with Chloe’s card directly above.<br>Chloe wins if <strong>no</strong> matches occur; otherwise Selena wins.</p>
</div>
<div class="specification">
<p>Chloe and Selena repeat their game so that they play a total of 50 times.<br>Suppose the discrete random variable <em>X </em>represents the number of times Chloe wins.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the probability that Chloe wins the game is \(\frac{3}{8}\).</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>Determine the mean of <em>X</em>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the variance of <em>X</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>METHOD 1</strong></p>
<p>number of possible “deals” \( = 4! = 24\) <strong><em>A1</em></strong></p>
<p>consider ways of achieving “no matches” (Chloe winning):</p>
<p>Selena could deal B, C, D (<em>ie</em>, 3 possibilities)</p>
<p>as her first card <strong><em>R1</em></strong></p>
<p>for each of these matches, there are only 3 possible combinations for the remaining 3 cards <strong><em>R1</em></strong></p>
<p>so no. ways achieving no matches \( = 3 \times 3 = 9\) <strong><em>M1A1</em></strong></p>
<p>so probability Chloe wins \( = \frac{9}{{23}} = \frac{3}{8}\) <strong><em>A1AG</em></strong></p>
<p> </p>
<p><strong>METHOD 2</strong></p>
<p>number of possible “deals” \( = 4! = 24\) <strong><em>A1</em></strong></p>
<p>consider ways of achieving a match (Selena winning)</p>
<p>Selena card A can match with Chloe card A<em>, </em>giving 6 possibilities for this happening <strong><em>R1</em></strong></p>
<p>if Selena deals B as her first card, there are only 3 possible combinations for the remaining 3 cards. Similarly for dealing C and dealing D <strong><em>R1</em></strong></p>
<p>so no. ways achieving one match is \( = 6 + 3 + 3 + 3 = 15\) <strong><em>M1A1</em></strong></p>
<p>so probability Chloe wins \( = 1 - \frac{{15}}{{24}} = \frac{3}{8}\) <strong><em>A1AG</em></strong></p>
<p> </p>
<p><strong>METHOD 3</strong></p>
<p>systematic attempt to find number of outcomes where Chloe wins (no matches)</p>
<p>(using tree diag. or otherwise) <strong><em>M1</em></strong></p>
<p>9 found <strong><em>A1</em></strong></p>
<p>each has probability \(\frac{1}{4} \times \frac{1}{3} \times \frac{1}{2} \times 1\) <strong><em>M1</em></strong></p>
<p>\( = \frac{1}{{24}}\) <strong><em>A1</em></strong></p>
<p>their 9 multiplied by their \(\frac{1}{{24}}\) <strong><em>M1A1</em></strong></p>
<p>\( = \frac{3}{8}\) <strong><em>AG</em></strong></p>
<p> </p>
<p><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\(X \sim {\text{B}}\left( {50,{\text{ }}\frac{3}{8}} \right)\) <strong><em>(M1)</em></strong></p>
<p>\(\mu = np = 50 \times \frac{3}{8} = \frac{{150}}{8}{\text{ }}\left( { = \frac{{75}}{4}} \right){\text{ }}( = 18.75)\) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\sigma ^2} = np(1 - p) = 50 \times \frac{3}{8} \times \frac{5}{8} = \frac{{750}}{{64}}{\text{ }}\left( { = \frac{{375}}{{32}}} \right){\text{ }}( = 11.7)\) <strong><em>(M1)A1</em></strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A biased coin is tossed five times. The probability of obtaining a head in any one throw is \(p\).</p>
<p class="p1">Let \(X\) be the number of heads obtained.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1"><span class="s1">Find, in terms of \(p\)</span>, an expression for \({\text{P}}(X = 4)\).</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">(i) <span class="Apple-converted-space"> </span>Determine the value of \(p\) <span class="s1">for which \({\text{P}}(X = 4)\) </span>is a maximum.</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>For this value of \(p\), determine the expected number of heads.</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><span class="Apple-converted-space">\(X \sim {\text{B}}(5,{\text{ }}p)\) </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p2">\({\text{P}}(X = 4) = \left( {\begin{array}{*{20}{c}} 5 \\ 4 \end{array}} \right){p^4}(1 - p)\) (or equivalent) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> \(\frac{{\text{d}}}{{{\text{d}}p}}(5{p^4} - 5{p^5}) = 20{p^3} - 25{p^4}\)</span> <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(5{p^3}(4 - 5p) = 0 \Rightarrow p = \frac{4}{5}\) </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Do not award the final <strong><em>A1 </em></strong>if \(p = 0\) <span class="s2">is included in the answer.</span></p>
<p class="p4"> </p>
<p class="p2">(ii) <span class="Apple-converted-space"> \({\text{E}}(X) = np = 5\left( {\frac{4}{5}} \right)\)</span> <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p5"><span class="Apple-converted-space">\( = 4\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally very well done and posed few problems except for the weakest candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">This question was generally very well done and posed few problems except for the weakest candidates.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A batch of 15 DVD players contains 4 that are defective. The DVD players are selected at random, one by one, and examined. The ones that are checked are not replaced.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">What is the probability that there are exactly 3 defective DVD players in the first 8 DVD players examined?</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 23.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">What is the probability that the \({9^{{\text{th}}}}\) DVD player examined is the \({4^{{\text{th}}}}\) defective one found?</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(3 defective in first 8) \(=\left( {\begin{array}{*{20}{c}}<br> 8 \\ <br> 3 <br>\end{array}} \right) \times \frac{4}{{15}} \times \frac{3}{{14}} \times \frac{2}{{13}} \times \frac{{11}}{{12}} \times \frac{{10}}{{11}} \times \frac{9}{{10}} \times \frac{8}{9} \times \frac{7}{8}\) <strong><em>M1A1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for multiplication of probabilities with decreasing denominators.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1</em></strong> for multiplication of correct eight probabilities.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Award <strong><em>A1</em></strong> for multiplying by \(\left( {\begin{array}{*{20}{c}}<br> 8 \\ <br> 3 <br>\end{array}} \right)\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{56}}{{195}}\) <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(3 defective DVD players from 8) \( = \frac{{\left( {\begin{array}{*{20}{c}}<br> 4 \\ <br> 3 <br>\end{array}} \right)\left( {\begin{array}{*{20}{c}}<br> {11} \\ <br> 5 <br>\end{array}} \right)}}{{\left( {\begin{array}{*{20}{c}}<br> {15} \\ <br> 8 <br>\end{array}} \right)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>M1</em></strong> for an expression of this form containing three combinations.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{\frac{{4!}}{{3!1!}} \times \frac{{11!}}{{5!6!}}}}{{\frac{{15!}}{{8!7!}}}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{56}}{{195}}\) <strong><em>A1</em></strong></span><strong style="font-family: 'times new roman', times; font-size: medium;"><em> </em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[4 marks]<br></em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P(}}{{\text{9}}^{{\text{th}}}}{\text{ selected is }}{{\text{4}}^{{\text{th}}}}{\text{ defective player}}|{\text{3 defective in first 8)}} = \frac{1}{7}\) <em><strong>(A1)</strong></em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P(}}{{\text{9}}^{{\text{th}}}}{\text{ selected is }}{{\text{4}}^{{\text{th}}}}{\text{ defective player)}} = \frac{{56}}{{195}} \times \frac{1}{7}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{8}{{195}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were two main methods used to complete this question, the most common being a combinations approach. Those who did this coped well with the factorial simplification. Many who did not manage the first part were able to complete the second part successfully.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">There were two main methods used to complete this question, the most common being a combinations approach. Those who did this coped well with the factorial simplification. Many who did not manage the first part were able to complete the second part successfully.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">At a skiing competition the mean time of the first three skiers is <span class="s1">34.1 </span>seconds. The time for the fourth skier is then recorded and the mean time of the first four skiers is <span class="s1">35.0 </span>seconds. Find the time achieved by the fourth skier.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1">total time of first 3 <span class="s1">skiers \( = 34.1 \times 3 = 102.3\) <span class="Apple-converted-space"> </span><strong><em>(M1)A1</em></strong></span></p>
<p class="p1">total time of first 4 <span class="s1">skiers \( = 35.0 \times 4 = 140.0\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></span></p>
<p class="p2">time taken by fourth skier \( = 140.0 - 102.3 = 37.7{\text{ (seconds)}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"><strong><em>[4 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">This was done successfully by almost all candidates.</p>
</div>
<br><hr><br><div class="question">
<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;">Four numbers are such that their mean is 13, their median is 14 and their mode is 15. Find the four numbers.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<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;">using the sum divided by 4 is 13 <strong><em>M1</em></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;">two of the numbers are 15 <strong><em>A1</em></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;">(as median is 14) we need a 13 <strong><em>A1</em></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;">fourth number is 9 <strong><em>A1</em></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;">numbers are 9, 13, 15, 15 <strong><em>N4</em></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;"><strong><em>[4 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A continuous random variable <em>X</em> has the probability density function <em>f</em> given by</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {c(x - {x^2}),}&{0 \leqslant x \leqslant 1} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Determine <em>c</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find \({\text{E}}(X)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) the total area under the graph of the pdf is unity <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">area \( = c\int_0^1 {x - {x^2}{\text{d}}x} \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = c\left[ {\frac{1}{2}{x^2} - \frac{1}{3}{x^3}} \right]_0^1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{c}{6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow c = 6\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({\text{E}}(X) = 6\int_0^1 {{x^2} - {x^3}{\text{d}}x} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 6\left( {\frac{1}{3} - \frac{1}{4}} \right) = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Allow an answer obtained by a symmetry argument.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates made a meaningful attempt at this question with many gaining the correct answers. One or two candidates did not attempt this question at all.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The probability density function of the random variable <em>X</em> is defined as</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {\sin x,}&{0 \leqslant x \leqslant \frac{\pi }{2}} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]<br></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\text{E}}(X)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^{\frac{\pi }{2}} {x\sin x{\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = [ - x\cos x]_0^{\frac{\pi }{2}} + \int_0^{\frac{\pi }{2}} {\cos x{\text{d}}x} \) <strong><em>M1(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><strong style="font-family: 'times new roman', times; font-size: medium;">Note:</strong><span style="font-family: 'times new roman', times; font-size: medium;"> Condone the absence of limits or wrong limits to this point.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = [ - x\cos x + \sin x]_0^{\frac{\pi }{2}}\) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">It was pleasing to note how many candidates recognised the expression that needed to be integrated and successfully used integration by parts to reach the correct answer.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Two players, A and B, alternately throw a fair six-sided dice, with A starting, until one of them obtains a six. Find the probability that A obtains the first six.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(six in first throw) \( = \frac{1}{6}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(six in third throw) \( = \frac{{25}}{{36}} \times \frac{1}{6}\) <strong><em>(M1)(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(six in fifth throw)\( = {\left( {\frac{{25}}{{36}}} \right)^2} \times \frac{1}{6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(A obtains first six) \( = \frac{1}{6} + \frac{{25}}{{36}} \times \frac{1}{6} + {\left( {\frac{{25}}{{36}}} \right)^2} \times \frac{1}{6} + \ldots \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">recognizing that the common ratio is \({\frac{{25}}{{36}}}\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">P(A obtains first six) \( = \frac{{\frac{1}{6}}}{{1 - \frac{{25}}{{36}}}}\,\,\,\,\,\)(by summing the infinite GP) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{6}{{11}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question proved difficult to the majority of the candidates although a few interesting approaches to this problem have been seen. Candidates who started the question by drawing a tree diagram were more successful, although a number of these failed to identify the geometric series.</span></p>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Two events <em>A</em> and <em>B</em> are such that \({\text{P}}(A \cup B) = 0.7\) and \({\text{P}}(A|B') = 0.6\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find \({\text{P}}(B)\).</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note: Be aware that an unjustified assumption of independence will also lead to P(B) = 0.25, but is an invalid method.</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A'|B') = 1 - {\text{P}}(A|B') = 1 - 0.6 = 0.4\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A'|B') = \frac{{{\text{P}}(A' \cap B')}}{{{\text{P}}(B')}}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A' \cap B') = {\text{P}}\left( {(A \cup B)'} \right) = 1 - 0.7 = 0.3\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.4 = \frac{{0.3}}{{{\text{P}}(B')}} \Rightarrow {\text{P(}}B') = 0.75\) <strong><em>(M1)A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B) = 0.25\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(this method can be illustrated using a tree diagram)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}\left( {(A \cup B)'} \right) = 1 - 0.7 = 0.3\) <strong><em>A1</em></strong></span></p>
<p style="font: 27px Helvetica; text-align: justify; margin: 0px;"><img src="data:image/png;base64,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" alt></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A|B') = \frac{x}{{x + 0.3}} = 0.6\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0.6x + 0.18\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.4x = 0.18\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(x = 0.45\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A \cup B) = x + y + z\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B) = y + z = 0.7 - 0.45\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 0.25\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 3</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{{\text{P}}(A \cap B')}}{{{\text{P}}(B')}} = 0.6{\text{ (or P}}(A \cap B') = 0.6{\text{P}}(B')\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A \cap B') = {\text{P}}(A \cup B) - {\text{P}}(B)\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B') = 1 - {\text{P}}(B)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.7 - {\text{P}}(B) = 0.6 - 0.6{\text{P}}(B)\) <strong><em>M1(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(0.1 = 0.4{\text{P}}(B)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(B) = \frac{1}{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p><span style="font-family: times new roman,times; font-size: medium;">There is a great variety of ways to approach this question and there were plenty of very good solutions produced, all of which required an insight into the structure of conditional probability. A few candidates unfortunately assumed independence and so did not score well.</span></p>
</div>
<br><hr><br><div class="specification">
<p class="p1">Consider two events \(A\) and \(A\) defined in the same sample space.</p>
</div>
<div class="specification">
<p class="p1">Given that \({\text{P}}(A \cup B) = \frac{4}{9},{\text{ P}}(B|A) = \frac{1}{3}\) <span class="s1">and \({\text{P}}(B|A') = \frac{1}{6}\),</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p class="p1">Show that \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(A' \cap B)\).</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>show that \({\text{P}}(A) = \frac{1}{3}\);</p>
<p class="p1">(ii) <span class="Apple-converted-space"> </span>hence find \({\text{P}}(B)\).</p>
<div class="marks">[6]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(A \cap B) + {\text{P}}(A' \cap B) - {\text{P}}(A \cap B)\) </span><strong><em>M1A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(A' \cap B)\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\) </span><strong><em>M1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A|B) \times {\text{P}}(B)\) </span><strong><em>M1</em></strong></p>
<p class="p1">\( = {\text{P}}(A) + \left( {1 - {\text{P}}(A|B)} \right) \times {\text{P}}(B)\)</p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(A'|B) \times {\text{P}}(B)\) </span><strong><em>A1</em></strong></p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(A) + {\text{P}}(A' \cap B)\) </span><strong><em>AG</em></strong></p>
<p class="p1"><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">(i) <span class="Apple-converted-space"> </span>use \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(A' \cap B)\) and \({\text{P}}(A' \cap B) = {\text{P}}(B|A'){\text{P}}(A')\) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>(M1)</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(\frac{4}{9} = {\text{P}}(A) + \frac{1}{6}\left( {1 - {\text{P}}(A)} \right)\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\(8 = 18{\text{P}}(A) + 3\left( {1 - {\text{P}}(A)} \right)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(A) = \frac{1}{3}\) </span><span class="s1"><strong><em>AG</em></strong></span></p>
<p class="p2">(ii) <span class="Apple-converted-space"> </span><strong>METHOD 1</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(B) = {\text{P}}(A \cap B) + {\text{P}}(A' \cap B)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = {\text{P}}(B|A){\text{P}}(A) + {\text{P}}(B|A'){\text{P}}(A')\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\( = \frac{1}{3} \times \frac{1}{3} + \frac{1}{6} \times \frac{2}{3} = \frac{2}{9}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong>METHOD 2</strong></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(A \cap B) = {\text{P}}(B|A){\text{P}}(A) \Rightarrow {\text{P}}(A \cap B) = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(B) = {\text{P}}(A \cup B) + {\text{P}}(A \cap B) - {\text{P}}(A)\) </span><span class="s1"><strong><em>M1</em></strong></span></p>
<p class="p1"><span class="Apple-converted-space">\({\text{P}}(B) = \frac{4}{9} + \frac{1}{9} - \frac{1}{3} = \frac{2}{9}\) </span><span class="s1"><strong><em>A1</em></strong></span></p>
<p class="p2"><strong><em>[6 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">A continuous random variable <em>X</em> has probability density function</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {0,}&{x < 0} \\ <br> {a{{\text{e}}^{ - ax}},}&{x \geqslant 0.} <br>\end{array}} \right.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">It is known that \({\text{P}}(X < 1) = 1 - \frac{1}{{\sqrt 2 }}\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Show that \(a = \frac{1}{2}\ln 2\).</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) Find the median of <em>X</em>.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) Calculate the probability that <em>X</em> < 3 given that <em>X</em> >1.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \(\int_0^1 {a{{\text{e}}^{ - ax}}} {\text{d}}x = 1 - \frac{1}{{\sqrt 2 }}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ { - {{\text{e}}^{ - ax}}} \right]_0^1 = 1 - \frac{1}{{\sqrt 2 }}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - {{\text{e}}^{ - a}} + 1 = 1 - \frac{1}{{\sqrt 2 }}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Accept \({{\text{e}}^0}\) instead of 1.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^{ - a}} = \frac{1}{{\sqrt 2 }}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^a} = \sqrt 2 \)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \ln {2^{\frac{1}{2}}}\,\,\,\,\,\left( {{\text{accept }} - a = \ln {2^{ - \frac{1}{2}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \frac{1}{2}\ln 2\) <strong><em>AG</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[6 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \(\int_0^M {a{{\text{e}}^{ - ax}}{\text{d}}x = \frac{1}{2}} \) </span><strong style="font-family: 'times new roman', times; font-size: medium;"><em>M1A1</em></strong></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left[ { - {{\text{e}}^{ - ax}}} \right]_0^M = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( - {{\text{e}}^{ - Ma}} + 1 = \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({{\text{e}}^{ - Ma}} = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(Ma = \ln 2\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(M = \frac{{\ln 2}}{a} = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \({\text{P}}(1 < X < 3) = \int_1^3 {a{{\text{e}}^{ - ax}}{\text{d}}x} \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = - {{\text{e}}^{ - 3a}} + {{\text{e}}^{ - a}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(X < 3|X > 1) = \frac{{{\text{P}}(1 < X < 3)}}{{{\text{P}}(X > 1)}}\) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - {{\text{e}}^{ - 3a}} + {{\text{e}}^{ - a}}}}{{1 - {\text{P}}(X < 1)}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{ - {{\text{e}}^{ - 3a}} + {{\text{e}}^{ - a}}}}{{\frac{1}{{\sqrt 2 }}}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \sqrt 2 ( - {{\text{e}}^{ - 3a}} + {{\text{e}}^{ - a}})\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \sqrt 2 \left( { - {2^{ - \frac{3}{2}}} + {2^{ - \frac{1}{2}}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{2}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award full marks for \({\text{P}}(X < 3/X > 1) = {\text{P}}(X < 2) = \frac{1}{2}\) or quoting properties of exponential distribution.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[9 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [20 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Many candidates did not attempt this question and many others were clearly not familiar with this topic. On the other hand, most of the candidates who were familiar with continuous random variables and knew how to start the questions were successful and scored well in parts (a) and (b). The most common errors were in the integral of \({e^{ - at}}\), having the limits from \( - \infty \) to 1, confusion over powers and signs (‘-’ sometimes just disappeared). Understanding of conditional probability was poor and marks were low in part (c). A small number of candidates from a small number of schools coped very competently with the algebra throughout the question.</span></p>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The random variable \(X\) has the Poisson distribution \({\text{Po}}(m)\). Given that \({\text{P}}(X > 0) = \frac{3}{4}\), find the value of \(m\) in the form \(\ln a\) where \(a\) is an integer.</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>The random variable \(Y\) has the Poisson distribution \({\text{Po}}(2m)\). Find \({\text{P}}(Y > 1)\) in the form \(\frac{{b - \ln c}}{c}\) where \(b\) and \(c\) are integers.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>\({\text{P(}}X > 0) = 1 - {\text{P(}}X = 0)\) <strong><em>(M1)</em></strong></p>
<p>\( \Rightarrow 1 - {{\text{e}}^{ - m}} = \frac{3}{4}\) or equivalent <strong><em>A1</em></strong></p>
<p>\( \Rightarrow m = \ln 4\) <strong><em>A1</em></strong></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>\({\text{P}}(Y > 1) = 1 - {\text{P}}(Y = 0) - {\text{P}}(Y = 1)\) <strong><em>(M1)</em></strong></p>
<p>\( = 1 - {{\text{e}}^{ - 2\ln 4}} - {{\text{e}}^{ - 2\ln 4}} \times 2\ln 4\) <strong><em>A1</em></strong></p>
<p>recognition that \(2\ln 4 = \ln 16\) <strong><em>(A1)</em></strong></p>
<p>\({\text{P}}(Y > 1) = \frac{{15 - \ln 16}}{{16}}\) <strong><em>A1</em></strong></p>
<p><strong><em>[4 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<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;">Events \(A\) and \(B\) are such that \({\text{P}}(A) = \frac{2}{5},{\text{ P}}(B) = \frac{{11}}{{20}}\) and \({\text{P}}(A|B) = \frac{2}{{11}}\).</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;">(a) Find \({\text{P}}(A \cap B)\).</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;">(b) Find \({\text{P}}(A \cup B)\).</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;">(c) State with a reason whether or not events \(A\) and \(B\) are independent.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) \({\text{P}}(A \cap B) = {\text{P}}(A|B) \times P(B)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A \cap B) = \frac{2}{{11}} \times \frac{{11}}{{20}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{{10}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({\text{P}}(A \cup B) = {\text{P}}(A) + {\text{P}}(B) - {\text{P}}(A \cap B)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A \cup B) = \frac{2}{5} + \frac{{11}}{{20}} - \frac{1}{{10}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{17}}{{20}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) No – events <em>A </em>and <em>B </em>are not independent <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>EITHER</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A|B) \ne {\text{P}}(A)\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\left( {\frac{2}{{11}} \ne \frac{2}{5}} \right)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>OR</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(A) \times {\text{P}}(B) \ne {\text{P}}(A \cap B)\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.5px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{2}{5} \times \frac{{11}}{{20}} = \frac{{11}}{{50}} \ne \frac{1}{{10}}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note:</strong> The numbers are required to gain <strong><em>R1 </em></strong>in the ‘<strong>OR</strong>’ method only.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </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;"><strong>Note:</strong> Do not award <strong><em>A1R0 </em></strong>in either method.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px 'Times New Roman'; min-height: 25.0px;"> </p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>Total [6 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>T</em> has the probability density function</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(t) = \frac{\pi }{4}\cos \left( {\frac{{\pi t}}{2}} \right),{\text{ }} - 1 \leqslant t \leqslant 1.\]</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) P(<em>T</em> = 0) ;</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the interquartile range.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) Any consideration of \(\int_0^0 {f(x){\text{d}}x} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">0 <strong><em>A1</em></strong> <strong><em>N2</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) <strong>METHOD 1</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Let the upper and lower quartiles be <em>a</em> and −<em>a</em></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{\pi }{4}\int_a^1 {\cos \frac{{\pi t}}{2}{\text{d}}t = 0.25} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \left[ {\frac{\pi }{4} \times \frac{2}{\pi }\sin \frac{{\pi t}}{2}} \right]_a^1 = 0.25\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \left[ {\frac{1}{2}\sin \frac{{\pi t}}{2}} \right]_a^1 = 0.25\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \left[ {\frac{1}{2} - \frac{1}{2}\sin \frac{{\pi a}}{2}} \right] = 0.25\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{1}{2}\sin \frac{{\pi a}}{2} = \frac{1}{4}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \sin \frac{{\pi a}}{2} = \frac{1}{2}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{\pi a}}{2} = \frac{\pi }{6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(a = \frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Since the function is symmetrical about <em>t</em> = 0 ,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">interquartile range is \(\frac{1}{3} - \left( { - \frac{1}{3}} \right) = \frac{2}{3}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>METHOD 2</strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{\pi }{4}\int_{ - a}^a {\cos \frac{{\pi t}}{2}{\text{d}}t = 0.5 = \frac{\pi }{2}\int_0^a {\cos \frac{{\pi t}}{2}{\text{d}}t} } \) <strong><em>M1A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \left[ {\sin \frac{{a\pi }}{2}} \right] = 0.5\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow \frac{{a\pi }}{2} = \frac{\pi }{6}\)</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( \Rightarrow a = \frac{1}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The interquartile range is \(\frac{2}{3}\) <strong><em>R1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 33.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">All but the best candidates struggled with part (a). The vast majority either did not attempt it or let <em>t</em> = 1 . There was no indication from any of the scripts that candidates wasted an undue amount of time in trying to solve part (a). Many candidates attempted part (b), but few had a full understanding of the situation and hence were unable to give wholly correct answers.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The continuous variable X has probability density function</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 24.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {12{x^2}(1 - x),}&{0 \leqslant x \leqslant 1} \\ <br> {0,}&{{\text{otherwise}}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine \({\text{E}}(X)\) .</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Determine the mode of <em>X</em> .</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{E}}(X) = \int_0^1 {12{x^3}(1 - x){\text{d}}x} \) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 12\left[ {\frac{{{x^4}}}{4} - \frac{{{x^5}}}{5}} \right]_0^1\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{3}{5}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(f'(x) = 12(2x - 3{x^2})\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">at the mode \(f'(x) = 12(2x - 3{x^2}) = 0\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">therefore the mode \( = \frac{2}{3}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p class="p1">Find the coordinates of the point of intersection of the planes defined by the equations \(x + y + z = 3,{\text{ }}x - y + z = 5\) and \(x + y + 2z = 6\).</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">for eliminating one variable from two equations <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>, \(\left\{ {\begin{array}{*{20}{l}} {(x + y + z = 3)} \\ {2x + 2z = 8} \\ {2x + 3z = 11} \end{array}} \right.\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">for finding correctly one coordinate</p>
<p class="p1"><em>eg</em>, \(\left\{ {\begin{array}{*{20}{l}} {(x + y + z = 3)} \\ {(2x + 2z = 8)} \\ {z = 3} \end{array}} \right.\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">for finding correctly the other two coordinates <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2">\( \Rightarrow \left\{ {\begin{array}{*{20}{l}} {x = 1} \\ {y = - 1} \\ {z = 3} \end{array}} \right.\)</p>
<p class="p2">the intersection point has coordinates \((1,{\text{ }} - 1,{\text{ }}3)\)</p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">for eliminating two variables from two equations or using row reduction <span class="Apple-converted-space"> </span><strong><em>(M1)</em></strong></p>
<p class="p1"><em>eg</em>, \(\left\{ {\begin{array}{*{20}{l}} {(x + y + z = 3)} \\ { - 2 = 2} \\ {z = 3} \end{array}} \right.\) <strong>or</strong> \(\left( {\begin{array}{*{20}{c}} 1&1&1 \\ 0&{ - 2}&0 \\ 0&0&1 \end{array}\left| {\begin{array}{*{20}{c}} 3 \\ 2 \\ 3 \end{array}} \right.} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1">for finding correctly the other coordinates <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p1"><span class="s1">\( \Rightarrow \left\{ {\begin{array}{*{20}{l}} {x = 1} \\ {y = - 1} \\ {(z = 3)} \end{array}} \right.\) </span><strong>or</strong> \(\left( {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}\left| {\begin{array}{*{20}{c}} 1 \\ { - 1} \\ 3 \end{array}} \right.} \right)\)</p>
<p class="p2">the intersection point has coordinates \((1,{\text{ }} - 1,{\text{ }}3)\)</p>
<p class="p1"><strong>METHOD 3</strong></p>
<p class="p2"><span class="Apple-converted-space">\(\left| {\begin{array}{*{20}{c}} 1&1&1 \\ 1&{ - 1}&1 \\ 1&1&2 \end{array}} \right| = - 2\) </span><span class="s2"><strong><em>(A1)</em></strong></span></p>
<p class="p1">attempt to use Cramer’s rule <span class="Apple-converted-space"> </span><strong><em>M1</em></strong></p>
<p class="p2"><span class="Apple-converted-space">\(x = \frac{{\left| {\begin{array}{*{20}{c}} 3&1&1 \\ 5&{ - 1}&1 \\ 6&1&2 \end{array}} \right|}}{{ - 2}} = \frac{{ - 2}}{{ - 2}} = 1\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(y = \frac{{\left| {\begin{array}{*{20}{c}} 1&3&1 \\ 1&5&1 \\ 1&6&2 \end{array}} \right|}}{{ - 2}} = \frac{2}{{ - 2}} = - 1\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p2"><span class="Apple-converted-space">\(z = \frac{{\left| {\begin{array}{*{20}{c}} 1&1&3 \\ 1&{ - 1}&5 \\ 1&1&6 \end{array}} \right|}}{{ - 2}} = \frac{{ - 6}}{{ - 2}} = 3\) </span><span class="s2"><strong><em>A1</em></strong></span></p>
<p class="p3"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Award <strong><em>M1 </em></strong>only if candidate attempts to determine at least one of the variables using this method.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[5 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">John removes the labels from three cans of tomato soup and two cans of chicken soup in order to enter a competition, and puts the cans away. He then discovers that the cans are identical, so that he cannot distinguish between cans of tomato soup and chicken soup. Some weeks later he decides to have a can of chicken soup for lunch. He opens the cans at random until he opens a can of chicken soup. Let <em>Y</em> denote the number of cans he opens.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) the possible values of <em>Y</em> ,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) the probability of each of these values of <em>Y</em> ,</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) the expected value of <em>Y</em> .</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(a) 1, 2, 3, 4 <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(b) \({\text{P}}(Y = 1) = \frac{2}{5}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(Y = 2) = \frac{3}{5} \times \frac{2}{4} = \frac{3}{{10}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(Y = 3) = \frac{3}{5} \times \frac{2}{4} \times \frac{2}{3} = \frac{1}{5}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(Y = 4) = \frac{3}{5} \times \frac{2}{4} \times \frac{1}{3} \times \frac{2}{2} = \frac{1}{{10}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> </em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">(c) \({\text{E}}(Y) = 1 \times \frac{2}{5} + 2 \times \frac{3}{{10}} + 3 \times \frac{1}{5} + 4 \times \frac{1}{{10}}\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = 2\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[7 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Candidates found this question challenging with only better candidates gaining the correct answers. A number of students assumed incorrectly that the distribution was either Binomial or Geometric.</span></p>
</div>
<br><hr><br><div class="question">
<p class="p1">A football team, Melchester Rovers are playing a tournament of five matches.</p>
<p class="p1">The probabilities that they win, draw or lose a match are \(\frac{1}{2}\), \(\frac{1}{6}\) and \(\frac{1}{3}\) <span class="s1">respectively.</span></p>
<p class="p2">These probabilities remain constant; the result of a match is independent of the results of other matches. At the end of the tournament their coach Roy loses his job if they lose three <strong>consecutive </strong>matches, otherwise he does not lose his job. Find the probability that Roy loses his job.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p class="p1"><strong>METHOD 1</strong></p>
<p class="p1">to have \(3\) consecutive losses there must be exactly \(5\), \(4\) or \(3\) losses</p>
<p class="p1">the probability of exactly \(5\) losses (must be \(3\) consecutive) is \({\left( {\frac{1}{3}} \right)^5}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">the probability of exactly \(4\) losses (with \(3\) consecutive) is \(4{\left( {\frac{1}{3}} \right)^4}\left( {\frac{2}{3}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>First <strong><em>A1 </em></strong>is for the factor \(4\) and second <strong><em>A1 </em></strong>for the other \(2\) factors.</p>
<p class="p2"> </p>
<p class="p1"><span class="s1">the probability of exactly \(3\) losses (with \(3\) consecutive) is </span>\(3{\left( {\frac{1}{3}} \right)^3}{\left( {\frac{2}{3}} \right)^2}\) <span class="Apple-converted-space"> </span><strong><em>A1A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>First <strong><em>A1 </em></strong>is for the factor \(3\) and second <strong><em>A1 </em></strong>for the other \(2\) factors.</p>
<p class="p3"> </p>
<p class="p4">(Since the events are mutually exclusive)</p>
<p class="p1"><span class="s1">the total probability is </span>\(\frac{{1 + 8 + 12}}{{{3^5}}} = \frac{{21}}{{243}}\;\;\;\left( { = \frac{7}{{81}}} \right)\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<p class="p1"><strong>METHOD 2</strong></p>
<p class="p1">Roy loses his job if</p>
<p class="p1">A – first \(3\) games are all lost (so the last \(2\) games can be any result)</p>
<p class="p1">B – first \(3\) games are not all lost, but middle \(3\) games are all lost (so the first game is not a loss and the last game can be any result)</p>
<p class="p1">or C – first \(3\) games are not all lost, middle \(3\) games are not all lost but last \(3\) games are all lost, (so the first game can be any result but the second game is not a loss)</p>
<p class="p1">for A \({4^{{\text{th}}}}\) & \({5^{{\text{th}}}}\) games can be anything</p>
<p class="p1">\({\text{P}}(A) = {\left( {\frac{1}{3}} \right)^3} = \frac{1}{{27}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">for B \({1^{{\text{st}}}}\) game not a loss & \({5^{{\text{th}}}}\) game can be anything <span class="Apple-converted-space"> </span><strong><em>(R1)</em></strong></p>
<p class="p1">\({\text{P}}(B) = \frac{2}{3} \times {\left( {\frac{1}{3}} \right)^3} = \frac{2}{{81}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">for C \({1^{{\text{st}}}}\) game anything, \({2^{{\text{nd}}}}\) game not a loss <span class="Apple-converted-space"> </span><strong><em>(R1)</em></strong></p>
<p class="p1">\({\text{P}}(C) = 1 \times \frac{2}{3} \times {\left( {\frac{1}{3}} \right)^3} = \frac{2}{{81}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1">(Since the events are mutually exclusive)</p>
<p class="p1">total probability is \(\frac{1}{{27}} + \frac{2}{{81}} + \frac{2}{{81}} = \frac{7}{{81}}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>In both methods all the <strong><em>A </em></strong>marks are independent.</p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>If the candidate misunderstands the question and thinks that it is asking for exactly \(3\) losses award <strong><em>A1 A1 </em></strong>and <strong><em>A1 </em></strong>for an answer of \(\frac{{12}}{{243}}\) <span class="s1">as in the last lines of </span>Method 1.</p>
<p class="p3"> </p>
<p class="p1"><strong><em>[6 marks]</em></strong></p>
<p class="p1"><strong><em>Total [6 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p class="p1">If a script has lots of numbers with the wrong final answer and no explanation of method it is not going to gain many marks. Working has to be explained. The counting strategy needs to be decided on first. Some candidates misunderstood the context and tried to calculate exactly \(3\) consecutive losses. Not putting a non-loss as \(\frac{2}{3}\) caused unnecessary work.</p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">The random variable <em>X</em> has probability density function <em>f</em> where</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\[f(x) = \left\{ {\begin{array}{*{20}{c}}<br> {kx(x + 1)(2 - x),}&{0 \leqslant x \leqslant 2} \\ <br> {0,}&{{\text{otherwise }}{\text{.}}} <br>\end{array}} \right.\]</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 20.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Sketch the graph of the function. You are not required to find the coordinates of the maximum.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 32.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the value of <em>k</em> .</span></p>
<div class="marks">[5]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em><img 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" alt> A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong> </strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for intercepts of 0 and 2 and a concave down curve in the given domain .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A0</em></strong> if the cubic graph is extended outside the domain [0, 2] .</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><em><strong>[1 mark]</strong></em><br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\int_0^2 {kx(x + 1)(2 - x){\text{d}}x = 1} \) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> The correct limits and =1 must be seen but may be seen later.</span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\int_0^2 {( - {x^3} + {x^2} + 2x){\text{d}}x = 1} \) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\left[ { - \frac{1}{4}{x^4} + \frac{1}{3}{x^3} + {x^2}} \right]_0^2 = 1\) <strong><em>M1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k\left( { - 4 + \frac{8}{3} + 4} \right) = 1\) <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;">\(k = \frac{3}{8}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 30.0px Times; color: #3f3f3f;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates completed this question well. A number extended the graph beyond the given domain.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 21.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Most candidates completed this question well. A number extended the graph beyond the given domain.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 25.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Tim and Caz buy a box of 16 chocolates of which 10 are milk and 6 are dark. Caz randomly takes a chocolate and eats it. Then Tim randomly takes a chocolate and eats it.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 22.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw a tree diagram representing the possible outcomes, clearly labelling each branch with the correct probability.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Find the probability that Tim and Caz eat the same type of chocolate.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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" alt> <strong><em>A1A1A1</em></strong></span></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[3 marks]</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 29.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong>Note:</strong> Award <strong><em>A1</em></strong> for the initial level probabilities, <strong><em>A1</em></strong> for each of the second level branch probabilities.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\(\frac{{10}}{{16}} \times \frac{9}{{15}} + \frac{6}{{16}} \times \frac{5}{{15}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{120}}{{240}}{\text{ }}\left( { = \frac{1}{2}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 31.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally well done. A few candidates didn’t take account of the fact that Caz ate the chocolate, so didn’t replace it. A few candidates made arithmetic errors in calculating the probability.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 19.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">Generally well done. A few candidates didn’t take account of the fact that Caz ate the chocolate, so didn’t replace it. A few candidates made arithmetic errors in calculating the probability.</span></p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 26.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">Jenny goes to school by bus every day. When it is not raining, the probability that the bus is late is \(\frac{3}{{20}}\). When it is raining, the probability that the bus is late is \(\frac{7}{{20}}\). The probability that it rains on a particular day is \(\frac{9}{{20}}\). On one particular day the bus is late. Find the probability that it is not raining on that day.</span></p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><img 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VJxHMfzvCiKRqMxPT399ddfD00FADEMAFAzSZJ8GRaKXC1mGGbLli1u19O9e3cawxaLRb629PR08njdq+pLsZMnTz799NOxsbHy2ZCys7PXrl1bxwpArSCGAQBq4CXYnJ5q27YtwzDR0dGPHj3ytCC5t5hlWZPJJL/OarfbWZblOK4uVSUN417uQSL/7dmzpyiKUVFR5BXVanVSUhIG4ggLxDAAQM28TGJIn5o9ezY5sxwyZIinRRwOR0FBASkWHx8vf5z0nTYYDF6WrVVt3YZxWVkZ+R0giqJKpWJZNicnh84HDKGHGAYAqAXXm4DJHydPnoyJiSFdnFyHtpAv9fTTT5OzYaPRSB9fsGABeZDEcMDt2LGjbdu2arWajhkiimJubu7OnTvR8zm8EMMAAD7xnlL5+fnkCmufPn28r6e8vJyU5Hn+ypUr5MHExEQSkKWlpXWPQ/kajh07lpeXp9Fo6J1UPM8XFhauX7/ebXkIMcQwAEDNajxlTElJUSqVJpOpxvV88cUXgiCwLMvzfEFBwaJFizp06EACUq/X375928ur+FhJ4tSpUzk5OTzP04E4BEHIz8/funWrw3PDNYQYYhgAwE8HDhxYu3btwYMHy8rKyNDQvXv3Jk95j+0JEyYwP8eyrFKpnDJlSkDS8V//+ldxcTG9OYplWb1eP2DAgNOnT3vqveWlthBUiGEAAF/RlNq6datGoyHnl/JBodVq9aJFi2hTs6dUe/z4cWJiojyGOY5bvHhx3Wv49ttv5+bmarXa6OhoEsMGg6FTp0579+51Wx+cE4cdYhgAwFckrq5cuWK32xkPOI5TKpWtW7fevn07XfD06dNOq7p79+7o0aOtVqvdbh89evSmTZtqzELvBc6ePVtUVESrQcak7Nu377Vr1/x9uxAKiGEAAJ/QFOzfv78oimSmYYVCQU466VDM8nbmXr16ffbZZykpKQzDZGRk1OVFXf9L/753796cOXNoDyyGYbRabdeuXY8dO+bve4XQQQwDAPiExp5TezJpmu7ateusWbPat29vNBpJQssbq1mWLSoqcl2Vp5fw/iz94+OPP27Tpg2ZnYn8DkhMTJw3b97+/fvRzlxfIIYBAGpBkqSdO3cmJCTQq8JqtXrgwIHyMkVFRQkJCbSHlNFodDtCpOt1WS+DhLiaMGECmQ+YjkbZrl27Or03CAfEMABArdFpGARBGD16NHnQKS8vXLiwZcuWcePGXbp0iT7opZHZ9RG3z165cmXYsGGxsbHkOrQoitHR0S1atFi5cqXbRSDCIYYBAGrt9u3bXbp0Wbp06VtvvUUe8SX/vISup7GgHT8/aR49erTBYOB5nrZ72+32iooKh7sma6gXEMMAAKFW29uEJEmaPn26/Jq0Wq1u167d2rVr5auq8VQbIhBiGAAgInhKzcmTJ8uvASsUitatW0+ZMqVWK4GIhRgGAAgp30+FZ8yYIYoi7YElCEJCQsKiRYuCX0cIHcQwAECo1ZjE48aNM5lMDMOIosjzvCiKWVlZFy5cCGEdIUQQwwAAoeO9a7TD4Vi4cKHNZmMYhvzLcVynTp327Nlz7969EFYTQgcxDAAQEV5//fXmzZvHxMTExcWxLKvT6dLS0mbNmhXuekFwIYYBAMJs5MiRFouF53nm37MhtWrVis4HjF5XDRtiGAAgdORXhW/fvj1t2rSEhASNRhMdHU36YaWmpu7fvz/c1YTQQQwDAISUJEmffvrpr371K41GQ3tBWyyWTp06LVy40G15R+1vNYb6AjEMABA6t27dmj17tnxaCNIL+vDhw16WQgY3YIhhAIAAqHFWhkePHvXt25dcAGYYhud5nufbtm27c+fOEFYTIg5iGAAgMLyMJTl8+HCe5xUKBZ1zKTU19bXXXgt5HSHiIIYBAPwnSZL3+QqHDBmSmpoaFRXFcRzLslqtNiUl5a9//atrSWicEMMAAH7yEqL/+Mc/BgwYoNPpeJ4XBEGpVIqimJycvGHDBt9XAo0BYhgAwH/0bJi6detWaWmpVqulPbBMJtPgwYM3btwYrkpCJEMMAwAExvHjx/v37y8IArkNSalU8jzfsWPHjz/+2MtSOBtu5BDDAAD+IyF67ty5wYMHC4JAzoAVCoVarc7Nzd20aZMDtxuBV4hhAAD/vfnmmz169BBFkQQwx3FWq3XOnDlbtmxxm77e/wuNEGIYAMCZl3SkT508ebJ169YkfZVKJcdxFotlxIgR+/btC1U1oSFADAMA/B9P9x3JH7l9+3ZJSYl8JCy1Wp2enr579+6Q1hUaBMQwAMDPeEnizz//vF+/fgaDgWVZ0g+L47i8vLxDhw7hAjD4BzEMAOCGU6Bu2rSpf//+cXFx8pPg/v37Hzp0yPuCAN4hhgEA3COB+uqrr2ZmZtKBoHU6ncViGTlyZGVlZbgrCA0BYhgAwA1Jkk6fPp2SkkICmDRB63S6goKCgwcPyou5LhjSikI9hxgGAHD2zTffDB48WKvVkvRlWValUhUUFJCRsHDTEQQQYhgA4P9IkvTqq6/yPE8DWKPR5Ofnnzx50qlYuGoIDQxiGADA4XA4jh07lp+fb7fb9Xo96QKtVqvbtWu3d+/ecFcNGjLEMAA0ZPS01csNRRcuXOjVqxeZiJBMxpCQkPDb3/722rVrnhYBCBTEMAA0cE5JLPfqq6+2adOGdIGm9wG3adPm/v37nhYBCCzEMAA0fK4jclRWVvbr148EsMlkUiqVOp0uOTn53XffdbsUQJAghgGggXPK4K1bt2ZnZ0dFRZGxoFUqlUajad269Y4dOxxe264BggExDAANH4nV1atX2+120vgcExMjCILdbn/++ec/+OADh4e2a+QxBBtiGAAavk2bNnXp0oXjODoOpSAI2dnZx44dc1se6QshgxgGgIZsw4YNiYmJer2enASTi8Ht2rU7cOAALePLtIYAQYIYBoD6x5d0fOedd/Ly8gRBIAEcFRVlMBg6dOiwYcOGENQQwEeIYQCol7zchrRp06Z27drR9mfaC3r79u0hryZADRDDAFDPeAngysrK1q1b03EoGYaJjo622+3z5s0LeTUBfIIYBoD6xPWGIvL3tWvXioqKlEolPQNmGKZNmzYVFRUOXOKFCIYYBoB6w22a7tu3r1+/fna7nZwBsyxrNBrbtGkzf/5810WQxxBpEMMAUF9VVlZmZ2fT9meWZTmOe+KJJ1xLys+hkcQQURDDAFD/nD59uqCggJGJjo5OSEhYvny5w0PQIoMhMiGGAaA+2b59e2ZmpkKhkGdwWlra8ePHSQFPcYsAhsiEGAaAWghBmHl6iZMnT7Zu3Zr5OYvF8uqrrwa7SgDBgxgGgP/jveU2BO26bi/i7tq1q6CggM5FSP5NTk6ePXt28GoCEBqIYQDwKVnDch48Z84cm81G7j7ieZ6cAet0uqlTp4ayYgDBgxgGgJqF+DzY4XD8+c9/bt68OW18jo2NZRhGo9FMnz79m2++CV41AEIMMQwADoeH2f1CNuWfPIPnzZtHpyMkV38ZhjEYDHPmzHnw4IGnOgPUU4hhAPj/wpVq9HUrKyszMzPl9yCRiYHHjx9/9+5dp8LIYGgYEMMA4CzE895LknTgwIFevXqp1Wp5L2iNRjNy5Mj79+97qQzCGOo7xDAA/MyFCxeGDBkSHx+fnZ1N5wQMXtrNmzePNDtTUVFRJpOptLT0xo0b8pJIXGiQEMMA8H+GDBkiT0SO46ZNmxaQNbuG6OnTp61Wq3w6QpZlk5KS3N6GhAyGhgoxDNBIuQbb0KFDVSoVnZ6InpsGcJZA+YsmJSXJI1+n0xUVFdVYSYAGBjEM0HjJQ+799983Go0kEZOTk2fMmFFcXEz+y7Ls/v37A/u6o0aNkmdwSkoK6YTlellakiQMBw0NGGIYoPGSd1HW6/XkHqG0tLQjR46Qx9u3b09isqSkJLAvOnfuXJrxpPV7x44dXrqGIYOhoUIMAzQuTjf8SJJ05MgRepPu0KFD5YXXrFlDnurWrVtdgtB12cuXL8fExJCpCWkY9+7de9asWTUuC9CQIIYBGhHXm2537NhBOyrr9XqnZ6uqqshT8qu2/uWi65lueXl5XFwcx3FkhCyKTFYI0EgghgEar8GDB8vz7ze/+Y1TgaqqKjKSc8+ePckjjx8/9u+1XM/CHQ7HrVu3pk+fnpCQQE+IieHDh/v5lgDqG8QwQOMiPyvt378/Tb7U1FTXwh999BGJ4U6dOjmC1j78/fffT58+3WQycRyn0Whop61Dhw4F4+UAIgpiGKDxopnHMMz58+ddC5w7d46cp/bt2zd41SDpvmnTpjZt2uh0OoZhRFEktercubO8jNsFAeo1xDBAI/XRRx/RDLbZbG7LrFu3TqFQKJXKCRMmBKkaTlH6+9//Xj6mB8Mwdrv9rbfe8r4UQP2FGAZojCRJGjp0KL0cO3/+fLfBtnjxYoZhlErlt99+G4IqkT8++eSTNm3aaLVaeRgPHDhQPri00yIA9RdiGKBxIX2sTp48aTKZaMcoTye7paWlDMPExcUFe14j1/WfPXs2KyuLVI80njdt2nTXrl1elgWojxDDAI3R8uXL5aNnLF682G2YpaWlsSybm5sbpGp4T9APP/ywdevWer1eqVSSUTZJn+1bt27RxZHBUN8hhgEaERpaOTk5KpWKNkrPmDHDtVh1dbUgCKIovv/++2Go67+r8dxzz5FRNvV6PTkt1uv1q1atwsTD0DAghgEao/T0dJrBLMu6bezdsmULy7Jt27aljwQ88GocL5o8fv/+/T59+qjVapZlae/u3NzcM2fOIIOhvkMMAzRGo0aNMhgMLMuq1WqNRrNs2TLXPEtJSdFqtYMGDXJExhnn9u3bW7VqpVQqyfiX5Jrx2LFjw10vgDpBDAM0Rjdv3uzQocOTTz7JMIxCoVi9erVrGXLe6fZEOYzmz59vMpkEQaCdqDMzM7/44gvyLOZignoHMQzQeM2ZM4ck2bp165ye6tevH8MwRqMxAiPt0qVL+fn5Wq1WrVbT+5qGDRtGno3ACgN4gRgGaEScThb/8Ic/kAzbt2+fvEBlZWVsbKxSqZw3b164quqdJEkrV65MS0tTqVRKpZK8i9atW58/fx4xDPULYhigcZF3MF6wYAHDMGq12vHzk8jU1FSlUimK4oEDByIw1WjHrqtXr44aNSopKYn22zKbzS+++GK4KwhQC4hhgMarvLycpNfXX39NH8zJyaHnl6IoVlVVOSK4pVeSpEuXLo0dO9Zms9G+31ar9aOPPqIFwltDAO8QwwCN17Rp08gNSzS05syZI59wkHSAcjtHYdg51WrWrFk2m02tVpOZmqKiogoLC3FvMUQ+xDBAY0RiiTRKMwyzZcsWh8Px8OHDxMRE8ojBYIiOjiaRnJqaevPmzUjIYKdXl4+iJUnSl19+2bx58/j4eFEUlUoly7KJiYnyTuAIY4hAiGGAxmvDhg0kdJcvXy5JUt++fcl/4+Livv3227t379psNvJIu3btHBF2Nky4Vmb37t1NmjQRBIGe1nft2jUsdQPwBWIYoH4IRvht27aNDIWxePHie/fukTEjGYYZPXo0KXDo0CE6Vsb06dM91SoSgllek4cPH/bv35/cy8SyrEqlSkxMdL0pCyASIIYB6oHAph1dz4kTJ8gpY15eXlZWFu2WJX+hZcuWkbEydDrdwYMHA1KBIHH6fP70pz8lJycbDAZSf1EUBw8e/ODBA0/lAcICMQxQbwQkNuSJLkmS2Wwm6Ut6R7MsW15e7vRaAwYMIGndqVMnL5WJkFSTV6OqqqpNmzYWi0Wr1ZK3YLValy1b5oiY2gIghgHqnzpGCF389u3b8fHxdIIHhmHS0tJcS966dSsuLo5hGEEQjh49WpeXDotNmzYlJycLgqBUKqOiomJjYzt16nTnzh0kMUQCxDBAvRHAs2H6h91uJzHcsmXLtLS0Dz/80O0LrVu3LjY2lgxvGdTqBRy9WvzUU0+1aNEiLi7OarWqVCqbzTZnzpxw1w4AMb23jIcAACAASURBVAzQyDjNLZiamkqmKqqurvZUnvxRXFzMcRzLsqWlpSGrre98+RGwZMmSrKwsURRtNhvpetatW7dPP/00cjqaQSOEGAaoT65fv56fn5+fn3///n0/Fne979ZkMpH7a92WlJf/5ptvLBYLy7JardZ1PX5UJhi8V0ySpB9//LG0tFSn06nVapVKRVoC5s6d61oYIDQQwwD1RnFxMR3cyukirh/IabHRaFQqlTab7fr1656K0b9XrlxJXr1nz56RlsQ1VkDeGl9VVdW1a1ee58nbUalUzz777OHDh4NfTQBniGGA+uHFF1+k41GwLGu1WgOyWnI2HBcXt3v3brcFnOItJSWF1OHMmTMBqUAYjR49OiUlhczRJAiCKIpDhw71vkjYf21Aw4MYBog4rsf6kSNHiqIo79IckJGh/vu//5tlWbPZrFKptm/f7kt9Jk+eTKoxcODAt99+u77HkiRJL7zwgsFgiI2NJdM02Wy2CxcuyAs4/V3f3zJEGsQwQKQrLCx0mm4hNTXVUbc8IMvOnTuXrvOzzz7zZcErV67QnwIcx/ldgYhy9uzZ9u3b63Q60kzNsuzIkSMdSFwICcQwQGSRH/p//PHHX/3qVxzH0VNhhmFiYmICchVTkqSoqCiyTtJFy5cROSRJ0uv1NIndlqkXXKu9efPmxMRE+lEbjUYy44Xj59eVvawBwA+IYYAItXv3boPBoFKpFAoF6Z9sMBhEURwwYIDf65Qnx5o1a2gHpQMHDpCnHj9+XOOy77//Ps/zLMvqdDrX1dYjTgOKkX+ffvrpuLg42vzQrVu3mzdvOurte4TIhxgGiERHjhxp3rw5y7Ik7UaOHHnx4kWHw3Hr1q0ADjqxdOnS8ePH0//WODsvffzrr7/euXNnoKoRCeTv/ZVXXmnRooVOp7NarQzDaLVaelrswBViCDTEMEDEmTp1akJCAsdxZJzn4uJi+bN1jAH/FvSe0PJ5f+sLt6fC8rc5duxYvV6vUCjIKJ6zZ88OY22hAUMMA0SW7t2763Q6URQFQdDr9Z07d5Y/G7JTMU9x68uz9ZHbHtEHDx7Mzs5Wq9Vk6ovk5GSMfwkBhxgGCAVP973IHz958mS7du3IJUme57Va7YgRI0JeU3A2ffp0s9kcFxfH8zzP8x06dNi/fz99tsaWfADvEMMAIeXpYL1t2zar1UoGOhYEISkpqV+/fjiyh57bz/zatWtPPvkkz/OkjVqhUMycORPfDgQEYhgg6Ny2JMuvRK5du5aMZqVUKkVRXLx4sXyiBRzuQ8b7R71+/XqTySSKokKhUCgUWVlZBw4c8GVBAC8QwwBB5MvAywMHDtTr9SSDdTpdYWEh2jnDyPtl7z179uTm5mq1Wnobt3z8S3xf4AfEMEDQeTo63717t6CggDREMwyj0+mmTp3qtBSO7GHhPYz/+Mc/arVa0o+dYRir1frOO+/4vh4AOcQwQCi4Ho7/9re/2e12hmFiY2MZhsnMzNywYUNY6gZ+OH78ePfu3Q0GA7labDKZnnnmmXBXCuolxDBAcLk9H5o9ezZp2CTT+5AjeH28+7YBc2qNcPvVrFy5MiUlxWg0ktE9mzVrtn79ek+FAdxCDAMEkdvD8dNPP00aMwVBEAQhKyvr9u3b3heBsPDxu5gyZYpOp4uPjydfa69evR49eoTvEXyEGAYIjBoHgCQKCwvJhHrk5uABAwbgeF3fSZK0Zs0au91OR6LW6/XLly93W9Lt39CYIYYBQuSbb77JzMwkE/hwHKfT6QYNGoRjcX1Hv8HLly+3a9eOJrEoik899dS3337r+Hn7NpIYnCCGAQLM7bF18+bNgiCQ6fPIv0uWLAl93SDY3n///czMTJVKRaYuVqvVkydPdiBxwTPEMEDQTZ06lZwEx8fHq1SqoqKi7777LtyVgiAaN24cvaNJqVTm5ua+++679FlEMsghhgECyfUI27lzZ4ZhyIjEBoOBTizoy8geEPk8jRZ+7NixrKwsOsoHy7J0lg581yCHGAYIopycHHqxcPDgwWfOnHFbDCN1NABuv8TJkyfr9XoyRxO5R7yiosK1GDRmiGGAQKKH14sXL7Zp04aeDD3xxBNeCjtwXG4Q3LZw3L9/v0+fPiaTifSQZ1m2X79+165dC1MdIeIghgECTJKkBQsW6HQ6EsAqlcppzmBohJYtW2axWGgDtUajwaBpQCCGAQKsW7du5FBLjrkDBgwId40g/CRJ+vHHH0tKSgRBUKlUZPS0vLy8s2fPysu4/dvTI9AwIIYBasfLsVKSpOzsbDJRUlRUlMlkmjJlituS0AiRbeDQoUPZ2dmMDLla7Kk8tpwGDzEMUAteMvj1119v2bIlObCq1WqbzTZx4kRPhaFh894NXpKk0aNHWywWcm+xVqvt2LHjuXPnfFwbNDCIYYAAWLp0KZmvkOM4tVqdlJS0adMmpzKYRRgcsm//448/7tmzJ/3dJori888/76W8A+fHDRRiGMAf8kz93e9+R8bGIoMJZ2VlnTp1qsYFoRFy/fZnzpyp1WppT4L+/fu7LYnNpgFDDAP4T5KkZ555JjY2tmnTpkqlUq1WFxcXy5/1tFSoKgiRyGlGy8uXL3ft2pV269Pr9YMGDaIlHYjkhg4xDFAL8pPgo0ePPvHEE1FRUVqtVqvVtmjRYtu2bb6vAUBu69atJpNJqVSS24vj4uIWLVokL4Atp6FCDAPUDjkaLl26VKPRqFQqq9XKMEyLFi3eeOONcFcNIpSP47R8/fXXAwcONJvNtBN1YWEhGegDGdyAIYYBvHF7+FuxYgUdh8FgMPTu3Tv0FYOGav369YWFhbSN2mAwrFu3Tl4AkdzAIIYBPHJ7ZW7QoEH0ZMVoNJaUlOCwCIFCt6UZM2YYjUaVSkXyOC8v7/jx496XwnZYTyGGAdxzPajduXOHDBNNemPFxcX96U9/wrEPAsVpW/qf//mfwsJCg8FAkphl2Xnz5jnQb6vBQQwDuOd0XPvwww+bN2+uVCo5jjMajS1atKisrHQtBlAXrjeXz507t0mTJvSOpubNm+/YscPTUlAfIYYBaiBJ0pw5c+Li4jiO43leo9G0atXqiy++CHe9oMFyitV9+/Y98cQTNIkZhpk2bZrbklAfIYYBPCL3dw4bNowc+wRB0Gq1hYWFjx8/duAICKEiSdKjR4/69u0rimJ6erpGo1EqlZ07d8YcTQ0DYhjAo6tXr6alpZHequTfVatWORDAEGje5wuhfx85cqSgoEB+R1OfPn1cF4H6BTEM4N7hw4dbt25Nj3cmk2nLli1uS+IgCIHiy7Y0Y8YMjUbDcRz5dWg0GpctWxaCukGQIIYBHA6XrjE7duwwGAwqlUqv1zMM071795s3b4a1ghC5/PsdVpepPs6ePZuVlcVxHJlQRKlU5uTkXLlypcaXw0/GCIQYBnA+Nq1bty4pKYlhmKioKKPROHPmzHBVDCKfH8HmNKa035YvX26329VqNQnj2NhYelrsFLqY3SuSIYahUXM9Ki1cuNBsNouimJiYaDQa5eP64hAG3tVqC6n75iRJ0oMHD7p27UpimJwW5+bmXrp0yeE5g7EZRxrEMMD/PzB9//33nTt3VqlU5M4Qo9G4ceNGnEZAMMgTse6b1sqVKy0WC8MwZIRznU5H+hIGZOUQbIhhaOzIceqdd95JT08nAaxUKpOSktasWeNUBkc0qBG5mc0LpxZpvzcq15V07dqVdqLmOK5Tp063bt1yWxIiCmIYwDF//nyVSiUIgl6vT0lJeeaZZ+7fv+9UBscvcEW2igcPHlRXV4f+dV0fqaioSElJISNRR0VFJScnO00LAREIMQyN3fjx40VRNJlMZIQsOlKgpyMdgNyFCxfi4+Ojo6P/4z/+w/el1qxZM3PmzIMHD96+fbvudXA63x0yZIjBYCAXjNVq9fDhw0+dOuVUEhtz5EAMQ6M2fPhwOkagXq9fsWKF/Fn5MQuHLXBrzJgxZPsRRfHIkSM1li8sLDQajbRHlUajmTt3bt2r4ZTEx48fz8rKEkWRZVmSx/PmzcM2HJkQw0HhejHG7Q6AazZh9NVXX2VkZIiiSA6IOTk5H330Eb4FqK2cnBw6xsuSJUu8F87IyCAlNRoN/f2XlZUVjIrduXOnb9++Op2ObuSZmZm7d+92LYnNPrwQw4FXY3ce/56CQJEk6fr16wkJCeTYxPP86NGj5c+GsW4QsTz9kuZ5nmxILMuOGTPG4a7hl/xht9tpYLMsa7VaW7VqRU6j33///SBVe+XKlSaTiVwtJl23BgwYEKTXAv8ghoPF7TWYM2fOjBs3rrS0dN++fV4uPSIJgmrp0qVqtZphmPj4eFEUFyxYEO4aQX1VUVHBcZxSqSSntiNGjPD0K7xHjx4KhYJkYUJCwsKFCx0Ox4svvkgWHD58uLxwAI8AkiRVVFSkpaWRW+FZlhUEITMz02laCBxzwggxHFzyjXvx4sVkZERyBta6devLly+7XnTE/lAXNbbzl5aWajQaOo/6jBkzQlg7aCBo1o4bN46RGTdunFMZitzRyzBMYmLitWvXyIOLFi0im+KUKVPcvkTdK0n+ePjw4bRp05KTk0nqR0VFKZXKIUOG3Lhxo46vAnWHGA4i+W6wdOlSeimI/jFx4kRPi0BdeArjgoIChmFsNptKpbJYLG6vkznwLYDPMjMzya86gpzjuvrrX/9K9nqe5ysrKx3/3sZWr15NFjx8+LC8fJC2wDt37vziF7+Ijo5mGKZJkyakPXz16tW4LT68EMOhsG3bNtojQx7GGo3G06Q9UHfyw8rFixczMjIEQWAYRqVStWrV6uTJk25L4mAEPvrqq6/k13ppFy3XTejKlStk28vMzJQ/PmHCBLLswYMH3S4YDM888wzpqk3qLAjCsGHDTp8+TZ7F9h96iOGge/TokclkIlu8Xq9PTU2Vt2LFxMSQYrglJnjeeuut1NRUcucGz/MTJkzAPcFQdwsXLlSpVFqtlud5pVKpUChmzJjh6S6Jnj17MgwzduxYh2xjy8vLY1lWoVDcvXvXdXhL/7ZJ12VdO52sXLmyefPm8gORRqP5y1/+4lQMQgMxHHRz584lGWwymS5cuHDp0iV6hZjYuHFjuOvYoDgdhhYtWkRv09RqtV27dsVRBuruwYMHGo1Gq9XSjlcMw5Ce0p7KDxo0yPHzkEtPT2c83LAUwGvDbh+vrq6eNm2a0WhUq9W0H3WbNm18ufUZAgsxHHhOWz8Zcp1hmM2bN5NHyBVKyrV3BvjB7UFn5MiR9HKAKIpejpIAtVJeXs6yrE6no627CoVi9erVvixLt9WuXbsyDDNp0qRg1tSbY8eOZWRkyJOYZdny8vJw1adxQgwHmNOpWK9evXieV6lUGRkZ9PEZM2bIY5iOnihfA3jn/VOSJKmqqiotLU2pVJIZkxITE0mrAz5e8INrGy9pTyY3DZNhUFmWpWNGelkPXVX37t3JmfS+ffuCV3NfvPjii82aNZMP9JGRkXH27Nnw1qoh8T58E2I4WCRJmjRpEtmmLRbLgQMH6OMvv/yyvK/WuXPnXJcNeX3rHy+f0htvvEHvDxEEobCw0Ht5AF/QEN29ezf9Gc3zvFartVqtSqXy66+/9nE9mzdvpmuwWq0rV64M8eQQtCb07/bt26vVarvdTu7l4zjut7/9raelMMiBHzx9aIjhwKMfcZMmTUiL9IQJE+QFhg4dSjOY5/l//vOfDmzNfnHbn6WiooJl2aioKIZhDAbDsGHDHjx4UPeeL9DIyTcbjuPoLkzapYm///3vPq6EnEzTBVmWbd68+bvvvhvEN+BDxX73u9+1bNlSp9NZLBaz2cyybGpq6qJFizzdSoBdKSAQw8Hyxhtv8DwvCEKTJk3og5Ik/fOf/yR37NF9+PLly2GsZ/3ldtiTkpISenSzWCx/+9vfPJUHqC26Ca1fv56eyPbo0YPneaPRKAgCue/Iu+rqavkw1PIwVqlUa9euDe57cOG0X5w7d+6pp56Kjo5Wq9VkTgiWZfPy8i5evOh9QfBOkiQy/bMrxHDgka2zdevWSqVSrVaTWxTo40899RTpDUEuwyQnJ7suC7VCPrQ7d+6Qe0IYhomPj+/evfuPP/4Y7qpBw+HUlJKfn2+xWLZu3bpw4UKGYZo0aaJQKI4fP17jejIzM+XRq9Pp0tPTaQ+p3r17B/dtuON62Nm9e3ezZs20Wi3tYcrzPKkbjlH+6dixI8Mwn3zyiesHiBgOioMHD5JhZjUajfxX5IkTJ8gQNoRSqST3MIDfyDb96aef0rlroqOjR40a5bYYQF243YpWrVpFYtVoNH799dc1bmnkfkWWZZVK5eLFi8mDJ06cIKeeOTk5nl4oGLx0HXr48GH37t2NRqNGozEajaQd3mq17tmzJzR1azBofyCGYZ5//nn54+QPxHBQLF26lDRYpaenyx8vLS1VKpUMwyQmJpITYtKDGuqiuLhYo9FwHBcVFaXT6Z577jlflkIwg++8jPdSWVlJYjgmJsaXblbvvPOO3W4fNmyY/MGDBw+SbDYYDIGqs9/kb/bw4cMFBQVarbZp06YWi4X8ehgyZMj9+/exB/mCDOhNrz4MGTIEZ8MhMmzYMPLbtmfPnvTBW7dukYl9rFYr/XEUCXtdvTZ06FDySarV6hYtWsyZMwdHBwilvXv3ktuWoqOjz5w5499KZs6cSTbjJk2aROAGXFxcHBcXl5SUpNfrlUqlUqlMTk6eP39+uOtVP3z00Ue0BVQQBNcCiOHAkyQpKyuLfOjz5s2jj48ZM4Y8OHLkyHfffZecDRsMBvQ89M7TZ/L111/LJ3Dt1KmTvDA+SQiNAwcOKJVKMlKbL9eG5ehWWlhYSDbjVq1aOT0VdqQmO3fuTEpKMpvNer1eq9WS04ysrKzr16+Hu4KRi3x0w4cPp4cpp7tmCMRwUCQkJJAb7+TXUWJiYhiG0ev1DofjwoUL5AQuISEByeGd28/n8OHDpInMZDIplcqSkhK3n97jx49DVEtorA4dOkQPsmvXrvVxL5YXu337tslk0mq1zL+nSoyEQ4HbOgwYMMBmsxkMBlJbcnq3Zs2a0FcvMrm9eEE+K5ZlW7Zs+ejRI9eSiOGgIJ97bGzs+fPnySNPP/002WrJ/N7Hjh0LY8fIesdp4960aRO96ctqta5atcq1cCQcyKAxuHTpEr3yV9vdmWylEydOJPdNKBSKCxcuyJ8KO9dqHDhwoGPHjkajMS4uTqVSkb6o+fn5VVVVnhZphOiHUF5eTn+l0fGMnY5RiOGgyM3NJV38169f73A45s+fT64eiaJ48+ZNh8Nx+vRp0tlh4MCB8gWxBddo8uTJdCDfrKyszz//3FHTKPYAwXPv3j16nO3evbvvmxwpOWLECPnijkjaaN3+oiX/HTx4cFpams1ms9lspPIxMTFTp06VF4ucNxJK9F2Tpjj65Q4aNOjhw4duSyKGg6JXr17ko09OTh4zZgzJYIZh/vCHP5ACe/bsIf2zOnTo4LRso918fTFo0CBy3sCyLLkYTMk/NLID4GOEEPjf//1feqjNz8+v1bJz586lZ9ItWrQIUg2D5Pjx42SgD/LeybtIT08P+xDZYUSOOfRa2JkzZ+i24aX7HmI4KE6ePBkbGxsdHS2/T18+nRmZnoXn+WeffVa+IJLDk4sXL6akpGg0GqVSabVax48f7/Ct/RkfKQTbrFmzyD6enZ3t4yKSJM2YMYMMucowjEqlWrNmTQRuqzVW6fXXX09MTCTdXFiWFQRBp9ONGjUqAt9LKJG3P3DgQPL9pqWlebmZDTEcFJIkLVq0yGQy0d+Jer3+6NGjtMBLL71Exj2eNm2aU5Y08s3Xrb179wqCwDCMVqvt0qXL/fv36VP4uCASFBUVtWzZksxK5GWbvH379qVLl1atWkVvpiD3CkfmbKc+7lxffPFFhw4dzGazSqWiczRZLJYNGzYEu4YRjn4aCxYsoA/ivuGQOn78eF5entFozM/PdxpNdPr06RzH8Tw/Y8YMB3oV/Zvbz2HPnj3khkWO49q3b49PCeqj5cuXM+4kJycfO3Ys3LULgFWrVqWnp8fHx9tsNjIEplKpzM7OvnTpUuPcZw8dOkRaQ5s1a3bjxg35U04fCGI4KDwNEUcfHzZsmEql0uv1y5YtC23VIp1TEpeUlJA7FDmOy8nJ8TQ2OkBkkh8KUlJSGIbRaDQkgKOjo/v27Xv37t0wVi+wJEl6+umnExISNBpNdHQ0GbaTYZhZs2Z5GTWzXoR0bSspSdKCBQtIa8eYMWPIfUqeVoIYDoPHjx+npKQIgmAwGEhXaqJebI5B4tox7dq1a6mpqbTrR5cuXcJVNwD/OMXMw4cPk5KSyG/KsrKyhhTADtmbffPNN1NSUkwmE+maSmatSE9PP3nypKelXP+OHH4EsMPhePjw4VNPPcUwTFJS0p07d+TrQaN0qHkaipY2SR0+fDgc9YpQ9OM6duxYkyZNBEHgeV6n05EBeOvRb2cAT65du0b+aEjbs2uaDh8+vGnTpmQIfTIthCAIzz77rJfT4nqhxqqSAtXV1dOmTSssLPSl3zhiOOhcv7aHDx/SHpKlpaWuJevRRhko8rf86quvxsbGks/HZrORAUExHhbUR41wX3b8+11v3ryZNGhpNBqdTqfT6ViWjYuLq6iocDTowx15Rz/99NODBw+c7hWWF6AQw8Hl6f53juPIJU9682tD+mnsH/Lex44dSybAsNvtGRkZly5dcjTujwXqLy/bbeQ3xgZEdXX1xIkTbTabQqHQarVk5G29Xm80Gvfu3Rvu2vnktddea9u2bdu2bcmslD6eDbv+7amMAzEccJ5aoZ1YLBbSXBMTExOSetUDP/30U48ePcjFYFEUjUbjli1b5AUa8NEKGpUGfCLo1qlTp9q0aaPX6wVBsFqtZB9XKBSDBw92RPyHMGzYMHoNcffu3b4s4uWcyu2DiOGgqPFHUFlZGem8sGPHjhqXagyOHj2alJSkVqsVCgXLsoWFhadOnXJbsjF/SgD1hetPjZEjR5rNZo1GYzQaSYsXwzBGo7G8vHzt2rXhq2kNevfuTUdh2rVrV11WhZ7SkeXGjRt0mO/aqu855PpT8fjx44mJiWRDV6vVxcXF4asdNHY+tiR7LxlAV69effPNN0tLS308FYtM5LP67rvvBgwYoNPpVCoVnaOJcGr6ki8VXu3ataOVHDt2bDBeAjHsJ1+uEPjX092XR+S/NCNhS/XElwveU6ZMIfcXsiybmJgov2IUyW8NGjynnSuwGSxJ0v379//2t7/NnDlz9uzZffr06dWrV1JSUmpqarNmzZo3b261WhMSEsg4GPS2vbq/biRYsWJFq1atDAaD00gmbu+idvsVhPJDuHnzpkKhIDUsKSkJxqsjhuvK085Z407r4+bly1ORyfUNun4mo0aNIp3GVSpVYWGhaxmA0PPey8bLru3pdyd55Ny5c2+88UZhYWFBQYHRaBRFUT7mPMMwcXFx8tClzbb0vxs3bgzsOw098lHcu3evc+fO5IYI+ZsVBIH0hPJxPSHw8OFDMp8jwzBTpkwJxusihgPA9QzV6Q+35V0frFUfvPrCy1GsU6dOtCF69uzZjpoOfwAh4GMGuz714MGDzz777MaNG0ePHv3DH/4wePDgwsLC3Nzc5ORks9ms1+vpTGs0eFiWjYmJkSexVqslxbRarV6vb9KkCb2MyjAMz/NBfe/B4/oDRZKkhQsX2mw2Mr4HpdFo6K+NGpsDQ4DMoEW+soqKCsRwxJEk6fHjx9euXbt8+bLD4fjwww9XrFgxcuTIoqKioqKivn37bt68edeuXYcPHz5x4sSZM2eqq6slSbp37x5Z/Icffjh37pzD4XjvvfcWLVr0u9/9rnv37p07dx48ePCIESPGjRu3cOHCZcuWLVmyZPHixfPmzZs0adITTzxhs9kqKytpBcL13mvk5XC2b9++zMxMQRDIAB0ffvihl2UBQqbGC8PV1dXff//9jz/++Pbbb69YsWLevHlPPvmk0WjU6XSiKJIJSLzjOE6hUAiCYLFYdDqdxWJJS0sjTdC//OUv//CHPyxdunTLli2vvPLK3r17v/jii88+++y9995LT0+32WzPPfdcCD+MIKKf8/nz5xMSEmJiYsgNnLSFwGAwfP/9945a/hIKhg8++IBlWZ1OJwhCkLqSIYb9V1ZWZjabOY5TKpVKpbKgoID9N/leR/+r1+ubNm0aGxtrMpn0ej2Zu16tVlssFnLtgZYkWyT9/UuKOe3M/fv3J9WI5MRy+9N1586dKpWKvFme53ft2uV7z36AkKmqqurXr9+oUaOefPLJnj179unTh0xdqlarPe3jTg/yPC8IgiiKWq1WEIQmTZoUFhYOHz583LhxR48evXDhgpdXp81jDbWJiL67v//97+3bt9fpdGq1mtxSTD5Pu91OBvrwtGxobNu2jQ5rv2fPnmC8BGLYT/PmzfO0E5KrCPRBennfZDI5lSQ3s5PJsMh4b/IV0uh1bbliWbZly5akJvVlzyT1HDFiBDljUCqVRqNx48aNvjfmA4SAJEkbN24kLaVkT5TvtgaDwTV0WZYlP8fJOW67du2ys7Pz8vIGDhw4dOjQl156iTaAOb1QbSvm34IRyPUtlJWVJSQkGAwGpVLJcRztR52VlbVp0yYvCwbbwoULGYYhR60zZ84E4yUQw346evSoPBp5nler1aRVymKxZGZmPvnkkwUFBV27ds3IyLBarbS1Kj4+3mg06vV6sj+bTCaz2WyxWBISEhITE5s3b96sWbPk5OSMjIx27drl5+enpKQ4NXaRo8Abb7wR7s+gZk77zLhx4+ghrKioyGnyL9fyAGHxX//1X/IfwfIkJj+yBUEwmUxZWVnt2rUbOXLkf/7nf54+fbqqquq7777zexv2ZcGGtIO4fS+DBw9OS0sTRVGtVms0GvqxT5w48ebNm6GvrJN3HQAAIABJREFUpMPh6Nu3Lz1rCtJLIIb9t3PnzoKCgj/+8Y9r1qwpKys7d+4cGUHU7eZ17ty57du3b9++/dChQx988MHu3bsPHjy4bdu2L774wuFwyOexd/XgwYMvv/ySzPH3ySef7Nq1a+3atZG5Q3rqNfqPf/wjOTmZtMPrdLqhQ4eGrYoAntENuKKiIj8/v2PHjrNnzy4pKcnLy+vWrduoUaOWLl26detWMmcOBMOmTZtSUlJI07T88pzdbncE/4eIa1dZOuxXr169gvSiiOE68eMmolptRpF/Wch7rcizR44csdls5DqZXq+vF+fx0JjhQknYzZ49u02bNk5d3l577TVH0L4LTz1USPsHOSMP0qsjhuvKx2+lLnf91urGpxDz1IuEPjJ9+vT4+HgylUXnzp3pLG+OyKg/gFs+3ugPgeV09CgqKhIEwWw2k56qLMu+/fbboazA0aNHyTUInufJXS3BgBj2n3zqvdqeBNc2gz0dAiLkcODp7GHevHmkWUmhUHTv3r26utrLIgCRwPd9GZtuMDg1C69atcpisSQnJ3McJwhCUE+FXVc+a9YscipcUFAQjNclEMN+8mNr8PRN+34+HYEB7PA8eknPnj1JBkdHR9P5HJ3KAESmGm+iwzYcVPKjii9T9gbk5Qj5+VVxcTE5C585c2YAX84JYjhgats67Ta9ahw9wCHbSiLhQOC2OfrixYvp6enkV6RGo5GPABcJdQaoldruqhAQTp+wPB1D84oOh2PAgAHkOBbUYUQRw3Xi951/bh/0JYPrWIEgkb+Fu3fvkvHoWZZNSEjYtm2b28IIZqiPcEIcGoHt6+o3m81G7lI7duxY8F4XMRxqnpK4Vhkcsb/Hd+7cWVxcTO72S0tLu3jxottiEVhzAMr7HoetN0IE+4tYsGABORXOz88P6osihuskgF+JH6fCkWbIkCF0fIPU1FTyII5c0MDUsZNHHReBkFm5ciVp1SsvL/dSrO4NJIhh/3lpXK3L3hWZe6b3g87JkydzcnLokDfPP/+892UB6invPyv9+NEZkDiHYJg+fTrDMGq1mo5F6vultFrFAWK4TjzdqOO2TI3r8VIyBN0TfOdUz3Xr1tG77LVa7Z///GdPJQHqOy87uH/HaKcH0XoUXvJPXq/XMwzTs2dPtxcNXb8pWqy2XyViuK7q3nnK+3cWIV2ZPL36jBkz6PRQ2dnZO3bsQA8saNicNuk7d+5UVVVdvXrV7bNQT7322mvk1GLMmDH0Qacv1yl3nZ7y/bUQwwFAPvFHjx5VVFT06NFjypQpy5Ytcy3gSVVVVc+ePc1m8+LFi/fu3St/ipwER9QPZHllxowZQwd9dboz2OFukw1ZJQGCRH5itGLFisTERKvVqlareZ7XaDTTp0/3fT2e/oCwe/ToERkAn2XZb775xrWA723OOBsOOvoRV1RUyGdGYxjGx0HXLly4IB80leO4oqIi8ss60m6NcKpDXl4eqXNcXJzTMNGubTgR1agOUEeSJPXr14/5OZZlVSrVwYMH/VjboUOHzp8/f+TIkYj6zd14ODVJklE7NBqN0Wh0+i4ePnx49uzZnTt37t+/f9asWeXl5StXriwtLZ00adLy5ctXrVq1a9euzZs3T506dfbs2SkpKcOGDavx1RHDAXDx4kXy00lu7ty55Fnve9SOHTuc9mQyo9aGDRucFo+oPbNVq1akwqIo1njqH1E1B6i7Ll26MAxjtVrJDktH/ydJXKu7Hk6cOCH/BU/Op7HLhB79zKurq7VaLc/zLMvyPN+hQwer1arVaqOiolynmnbLqVjv3r29vzRiOABKS0vpJ96pUye73R4dHZ2env7gwYMal124cCH5zvLy8oYNGyafUWT48OEhqLyP6Db63nvvtWjRgkxynpWVdeXKlfBWDCDEysvLGdk8xNnZ2adPn96/fz/dc48ePVqrFfbs2ZMuS6cQQBKHhSRJBw4ccApUpzmnKfk8jJ4ymGEYi8Xi/UURwwHQsWNH8tH36NHD4XDs2rWLfPrkbjPvZ4fXr18nhcl/v/vuu27dutGvMysry+1SoSR/3Tlz5tBtq02bNjdu3AhLlQDCKD8/n+wCKpVq+/bt9PGEhASGYaKiojZt2uTjqmbOnJmVlbVy5colS5ZoNBqyWr1eH7zJfKBGoii6hqtTKmdlZWm1WoPBkJqa2q1bt169ek2ePLl9+/bdunXLzMwk80FRkydP9v6KiOE6IRFVVFTEMExiYiJ5cMeOHTExMQzDFBcXy4s55ej169dJjK1evXrIkCHykj169KDfOhkMMlxXjOSvmJubq9VqyYbYp0+fENcEIBJs2bKF7JtRUVHygVolSbLZbGTvWL16tZc10H159erVZFVGo/GHH344e/ZsXFwceaRdu3ZBfyfgzsSJE51CNzEx8cUXX9y4ceOsWbMmTZr09ttvHzlyxHVBp6uHr7322v/+7/+Wl5cvWrSoxhdFDPtJ/qGvX7/earWePXuWPLJmzRrSWDF16lS3y27YsEGtVpPdz+EhXEePHk02hVatWjm9Ygg4bVJVVVUZGRksy+r1ekEQSktLQ1YTgIjSvn17ckXm17/+tfzxn376iVwhZll2586d3ldCdqu5c+eSfZznefL4/v376WWpkpISTwtCkFRVVZFLwuR7tNlsTp1PHV7v+a6xmCeI4Tpx+1lv2rSJ7Ei7du1yu0heXh7t2eFphZIkJSYmkvWsXLkyZLufa4+wdevWabVaUhODwfD++++HpiYAEYi0PJvNZqfH//nPf5IdhGGYDz/80JdVTZo0iexWoijSB2fPnk3PxtauXevAjX8htH79enplt3v37vKnnLpSe+85W9t+tYhh/7neUET+XbFihUqliouLcy1J/mjRogX5tVVcXOzle3rhhRfIhSJfurwHkLxK8+fPp9tldna224k/ARqPmTNnsiz7zDPP0EfI/vLpp5+S3USj0fi4qi5dupCdq2XLlnRVkiR1796drCo9PR0ZHEqSJEVFRYmimJiYeObMGU9lvPzX9SncNxwemZmZDMN07drVUwG73U5aorw3Xh04cECr1cbExIwYMSLwtfSKbDqlpaXkMMFxHOl95qj9Dz2ABubll1923fjXrVtHflvTSU1qlJOTQ+I2Ly/P8fMdivYSmjdvXqCqDb64dOnShg0b7t+/7/ca/DgwIobrxPX3zsGDBzmOY1mW3Cvm9itp0qSJQqGIjY29evWql4sKhw8fFgRBEITQx7DD4Xj22Wejo6NJBk+cONGB3IXGzdPIheS/qamp5DdrWVmZjyskMcyybFFRkXxVDodj4MCBJIbdNqpBsNX4UTudjXg68UWjdHgMHz6cZVmWZZcsWUIecfomtm/frlarWZZNT0+XF3D9wuiNT0OHDnVbIEgePXrUrl07coBQq9UrV64M5asDRDJPO0Lz5s3JLnPo0CEfV5Wbm+v2MqTD4di8eTPDMORAce3atTrVGIImUDewIIYDrEePHjzPi6JImzWcvqRTp06RFqfk5GTvq9q+fTvZS3v16hWs6rooKyujN71lZ2d/8sknDmQwwL+5HWK2oqKC7DL0rkVf9OrVi2VZpVJps9mcnrpy5QpZIcdxZJY91wFiocFADAcMbZsSRdFkMrn+UCJ/Hzt2jPzIle97bncw0jDFsuzy5ctDU/kTJ07Qi8GDBg3yVDGAxsbT7nzy5MmFCxdarVby29put1dXVzuV8bTCsWPHki5dCoXi9OnT8qeOHDlCYlipVNKpBdAto6FCDPvPda84cuSIKIosyzrdUyjfbQ4dOkTu/9FqtV7W+a9//YsUY1k2NEPqvPLKK6RzmV6v/+ijj0LwigD1iGv4jRw5UqPROA01rNPp9u/f72Vx+a2AdMEJEybI1z916lSS0Dqd7rvvvnP76tBgIIYDRpKkIUOGcByn1Wrl+6HT/nP//n0ym7RWqyXNTa7FJElatWqVSqViWbZDhw6uKwmsb7/9tmnTpiTyzWaz/K5H7PwAcvS0ODc3l87oIEeStX379jWu6tGjR2azmRwNyEg+9CXID2KO46xWqwO7YUOHGA4k0jC1YMECh4drSESTJk2ioqJMJpPbAuTv/v37k72aztQUJJcvX6adPLOzs7/66iunAjgEADiRT8YgT185chuSF5IkTZgwgWEYlUrFcdzs2bPpU2SFSqVS3okae2JDhRiuE/mO8fLLL3McJx9ex1M/ul/84hdkQrTDhw97KkaH0Nq8ebPblQTE3LlzyTm3QqHIzc11fVMA4GT+/PnkpkSNRkOGrWVZtmnTptevX1++fLlWqyVNYgzD2Gw2t/2c5bsYmdGBZVl64rts2TIa7Rs3bnR7bww0JIjhACA7RnFxMc/z3gfGcjgcjx8/LiwsJLvZqFGj3O5aixYtIt2V9Xq923uLA1LhJUuWkAFsFQoFpmoA8FFhYSE59yVDV0ZFRQmCQPpRSpJUWVlps9lo36ukpKRRo0a1bdvW7ahMkiSRy8BEbm4umUWR6Ny5s9sKIIkbGMSw/5wStHv37hzHPffcczUuSHpIMp7nKUpNTSW/helElQHc8SRJqq6uTk1NJRncpEmTqVOnYsw8AB/17duX7J50GoYWLVrIC1y9ejU7O5thGPmUeT179qQFnPYvq9UqCIJOp5O3b6tUKtd5BaBBQgwHxr59++Lj4xmGeemll7wUI7vfxo0bSVtWSkqKa4GTJ0/SXXfFihX+1cdTjkqStGXLFtIrhPz6/sc//uHfSwA0QlVVVSqVimEYpVJJ/tBoNJ9//rnTHnf27FmTySS/Zjx48GD6rFPhc+fOZWRkOF1gHjNmTIjeEoQbYriu7t69++WXX5J5VwwGg9NgpG7jUJIkk8lEri253ow0cuRIsh86dZ70tDZPr+V6g4QkSSNGjFCpVKTRrH379jjrBaiVlJQUkpccx8XExERHRw8cONDtHb179uzJysoi+zIZ2tbhslfK/zt06FCr1Wo0GlNTU0tLS7FvNh6IYf+9+OKLTZs2pT0sGIbp37+/a7HHjx/L/0v2LtLTkmXZzMxMp/LkXgWGYUaPHi1fypcM9p7WgwYNYhiGnIj37dvXpzcJAP/27bffys9xyQ1+9Fm3N0ccOnRoz549XtaJuAXEsJ/ee+89g8HgdJfCtGnTaAHve9eBAwfUajXZk+fPn08L0xshWJb9+OOPa7WLesng6urq1q1bkzVbLBYyVYMv9QQASpIks9lM9nqe561WK73J3ssQV16uEPlYEho2xLCfJk2aRLtUUBaL5Z133vGylHw3y8vLIxeWlErl9OnTDx06RHtgMgwzfPjwQFX17NmzpMMIy7J2u/3kyZM11g0AnJAdZM+ePeQKVGJi4tq1a+VP+Rer2O8AMeynsrIy0k9Sq9UqFAp5GE+aNMnTUvJd7s6dO+QOfdJhSqlU0paugoKCgOyckiQtXLgwKiqK/HhPSUn517/+5aVKAFCjGzduyE+Ca9yDarwNwctQP9AYIIb9NGbMGNJPkud5rVZLJgZmGIZcOsrIyPBlkuAjR440a9ZM3rKt0WhSU1N/+uknWqa2u6X8h/n48ePJXROiKBYXF3sqBgCB5X3MDR/7WmL3bCQQw36aNGkSubjLMIzVau3Tp8+cOXPsdrv8zj9fGpavXbvWunVrvV4vCELr1q3l14kp//bGgQMHKpVKg8HAcVy3bt08FcOuDlAXvvSO9PIUToUBMeynGTNm0FNYu91+/fp1h8Nx7Ngxck5MxsBiWXbXrl2+rO3q1at37971uzKuezKdAFWr1ZaVlfm9ZgAACCrEsP/S09PJWe+wYcPog5cvX87JyaHtzL7PGFjblihPdyQvWLAgLS2NVMBoNG7cuNH7IgAAEEaIYf8dPnzYarVOnjzZ9akdO3YMGDCAzNxQo7qnI20QmzNnDm0St1qttFM0AhgAIDIhhuukxktBtTq19X0RtyVnzpxJGsPpSHi1XS0AAIQYYth/3puR69K27Psi9O+BAweSAFar1VOnTvWyfuQxAEDkQAz7z/Ussy53GtT2nJWW/OqrrwYPHkwy2Gw2v/nmm57qgAAGAIg0iOGACUvI7d27V6fTiaKoUqnS09MvX77svTJIYgCAiIIY9hMdPSewwVartc2dO5fccKzX67t27ep0yxPOhgEAIh9iuL6aOXMmmStJpVKVlpaGuzoAAOAPxHCE8nSZmfy3c+fOPM/zPG+3271PJgEAAJEMMRy5XEeNlyRp48aNNptNqVSq1ery8vJLly6Fq3oAAFB3iOH6ZOvWrRzHsSzL8/yAAQPIg7jiCwBQfyGG6405c+bQMTJ/85vfYFAOAIAGADEc0WjWTpgwgWSwTqdzO3wmAADUR4jhyEXPdOfMmUM6RZtMprlz5zpqP9YHAABEJsRwRPvggw/sdjvP8yzL5ufnh7s6AAAQYIjhiODpvPYXv/iFIAiiKI4cOTLEVQIAgBBADIeZ2yGpiXbt2imVSr1ej9E5AAAaKsRw+LmeCu/du9dms7Esa7FYDh48GI5KAQBAKCCGIwXtdVVRUUE6ZNlsthMnTsifBQCABgYxHGbyfK2oqNBqteTO4KZNm965c8dLYQCA/8fe/cfHcCf+A3/PzuxsZje72bW7dmXTpEmTNJFUfKSJBC1FOa40jlTQ0CjFyYeKcnIoH1GONspRVKuHq8pF27ScXhWnpaWUQ+XaT/XTnh6Oo189raocZr5/vO/mpvsrm81mf76ef3jE7Hsm793MzGvfM+95vyEKIIbDRUNDQ2pqKp2qYfv27a4FkMEAANEHMRxiNFwHDx7MsqxGo9Hr9WvWrPFUDEkMABBlEMOhN336dIZh9Hq9w+F46623Ql0dAAAIHsRwUCkbtfTfdevWEUJ4ns/Ozr58+bKyGAAARD3EcJto9hqyKIp/+tOfBgwYIAiCRqNZv349LjsDAMQgxHCANZujtMC2bduMRiPDMBzHzZkzR/I6jgcAAEQrxHDgNRuiM2fOFASBEKLX6zds2CC5u1gNAACxADEcYHKIekrT5cuX0wvRdru9sbHRdUUAAIgdiOE24SlTJ0+eTAjR6XSzZs2S3GU2whgAIKYghoPk8uXLJSUl9EL0okWLXAsgiQEAYhBiOMBce1pdvXq1f//+Wq2WZjCeDAYAABli2E+ubVa3rdh33303NTVVp9NxHDdq1KigVA0AACIGYth/zV493rRpE52nQc5gPJUEAABKiOG2Mm3aNIZhCCFxcXHl5eUSOmQBAIALxHBruX3Y95VXXqFzBttstm3btoWoagAAEO4Qw63i2py9fPlyr169BEEQBKFjx45HjhxxLY9GMAAAUIjhAJDD9b333uvYsSMhhGGYn/zkJ4hbAADwDjHcKsq7vHV1deTfampqvBQGAACgEMMB8N133/Xv358GsNVq3bVrl6eSSGIAAFBCDLfW6dOn77zzTo7j6CiVJ06ccC2D9AUAALcQw75y7V1Ff87NzaVPJdlstt27d3taEQAAwBViuGWUYXzo0KFhw4bRDlkPPvjguXPnXEsCAAB4gRj2iWtTeM6cOQaDgd4PXrBggdvyAAAA3iGGW0wUxVmzZhmNRpZlBUGYPHmyl5LBrBgAAEQcxHDznNK0qKiIEKJSqXJycjBdEgAAtAZiuBlOGVxWVkYIMZlM/fv3/+GHH7ysgoGjAQCgWYjh5smxOmPGDNohq7q62lNJhC4AAPgOMfwfXhJ027ZtdrudPhk8d+7cYNYKAACiGGLYGxrMtbW1Op0uLi4uIyNj586daO8CAECgIIabMX78eI7jeJ7v3bt3qOsCAADRBjHszcKFC+nN4HvvvVdeiNYwAAAECmLYvalTp7IsSwjheX779u2IXgAAaAuI4f+Qs7Zr167ydEkbN250LQAAABAQiOH/oCnbuXNnQohGo+ncufOpU6ckdyNZAgAABARi+EdGjx5N28H3339/qOsCAADRDzH8L9evX6ejVOr1+qqqqlBXBwAAYgJiWJIkaePGjVqtVhAElmWXLFmC688AABAcMRrDyqCtrq7WarUGgyE7O3v//v2uBQAAANpITMfwtm3bsrOzeZ7XaDS5ublXr15VvgoAANDWYjSGJUn605/+ZLPZ1Gq1Xq8vKSlxehVJDAAAQRCjMfz9998nJiYyDGO1WpcuXSovV6YvkhgAANpazMWwKIqHDx9OS0sjhLRr1+79999XvuT0AwAAQJuKuRh+9dVX9Xo9x3EFBQVeiiGJAQAgCKIhhn2JTFqmd+/edrvdYDBUVVWdO3eu7asGAADgTTTEsI/oSNEOh2Pbtm0YnxIAAMJBNMRws2l66dKl4uJiQojZbH755ZdbtC4AAEDbifgYbrZdu3r1aoPBQAh59NFHndYCAAAIrYiPYZlTHtMfqqur4+Li4uPjR48e7X1FAACA4IuGGPaUozU1NYQQjuN++9vfupbEI8IAABBy0RDDMjlNT548mZSURAixWCwHDx6U8EwwAACEpeiJYTlfa2trNRoNIaSoqOiHH35AqxcAAMJW9MQwtWnTJo7jCCGTJk1SLkcAAwBAGIrIGHabqaIozp07Nz4+nhDyyCOPeCoGAAAQPiIyht2aNGmS1WqNj49/+umnlcsxUgcAAIStiIlhL32smpqaunfvTghJSkrau3ev27XcrggAABBaERPDnmzYsMFkMmk0mi5duty8eZMudEpcBDAAAISniIxh+TpzdXU1wzCEkGHDhrmNXrSGAQAgnEVkDFN9+vTR6/VGo7GxsdFLMdwbBgCAsBWRMXzgwAGr1WowGFJSUnbv3h3q6gAAAPgpwmJYFMWKigo6Okd2dvaZM2dCXSMAAAD/hWkMe7qGPGzYMEIIy7IVFRVBrhIAAEDAhWkMU8rbujdu3EhOTiaEaLXaRYsWKQsAAABEqLCOYdn27dvphejMzEx6MxgBDAAAUSDcY1gUxZdeesnhcJhMpgEDBsgLnX4AAACIROEew2PGjBEEQaVSlZWVKZcjgAEAIAqEdQz36NGDEEIIWbhwYajrAgAAEHhhGsNffvml2WymnaJfeumlUFcHAACgTYRjDG/fvj0xMZEQotPpdu3aFerqAAAAtJXQx7DTXd7S0lK9Xk8I6dev3/nz592WAQAAiA6hj2FJkbLFxcWEEIZhJk6ciOgFAICoF8oYVo7OIYpiUVERvRD9xhtvYD4GAACIBWHRGt6+fXt6ejrLsnq9funSpchgAACIESGLYTllN2/erNPpOI4zGo24Fg0AADElxK3hDRs2qFQqQkjnzp3ffffd0FYGAAAgyEIZw2PGjNHpdISQvn37ujaC0SwGAICo1yYx3GyCnjt3zm638zxvsViWLl3aFnUAAAAIf4GMYV/ar6IobtiwQaPRqFSq/Pz8W7du+bgiAABA9GnDi9JurzNXVlZqtVqGYUpKSpotDwAAEN2Cd2/46tWrmZmZdKqG7t2704WIXgAAiGUBi2HvgXrhwoWkpCRCCMdxq1at8mUVAACAqBeM1vC+ffusVivDMF27dj1+/LjTqwhjAACIWQGOYadMFUVx8uTJcXFxDMMMHz68ResCAABEvbbtotW/f396M7hfv35NTU2Sh6yVFyKJAQAgprQqhr2nZn5+Ps3gqVOnIl8BAABc+RPDTjMjuRbYt2+fw+FgGEaj0Tz11FNOKwIAAADV4hj2EqX0pSVLlvA8Twix2WyHDh3yZUUAAIDY5H9r2O1/16xZQwhhGCY3N1f5KuYuBAAAcOVna9g1UE+cOJGXl0czuFOnTrRDlusqSGIAAABZYHpKL1y4UKPR0AwePny4suczchcAAMCTANwbHjZsGA3g1NRU5c1gAAAA8K6194ZLSkoYhqEPJq1ZsyZwFQMAAIh+rbooXVRURAOY5/mNGzfShbgKDQAA4CM/Y3j9+vVarValUjEMk5KS8uGHH0oIYAAAgBbyFsOeYnXRokXk34YNG4b0BQAA8I/HGPY0znNlZSXDMAzD8Dz/i1/8Qi6jLIZgBgAA8EULLkpfunRp+PDhtFM0IWThwoVui+H5YAAAAB81H8M0UDds2GA0GumFaJ1Ot3jx4mZXAQAAAO+aiWEaqCNGjLDb7VqtlmGY/Pz8s2fPSs1lLdrEAAAAzfIYwykpKYsXL16xYoVer6eNYIZhZs2a5fumkcEAAADe/SiG5eDMzs4mhLAsazAY5AweMWJEKGoIAAAQtYjbq8c0fdPS0jiOozE8c+ZMpzUxYQMAAEArEenfIXrr1i368+9+9zvyY6mpqW5XRvoCAAC0hpuL0s8995w8TLTsvffe8xS6CGMAAAD//CuGnQbrKCgoUKvV8iPChJA333xTuZrTtWgkMQAAgB/c9JSmmbp69ep27drxPE9jOC0t7fDhw5JL4iKAAQAA/Ob+gSUarocPH3Y4HFqtliZxQkJCXV1dcKsHAAAQzTy2hqmbN28OGjSIjp/FMIxare7Ro8c333zjtjAAAAC0iE8zLC1fvtzhcLAsS/M4NTX1+++/91QeN4wBAAB81PwMS/TngwcPZmVlyR2ns7Kynn76adeSblcHAAAAt3yKYVlpaWl8fDxNYr1e/8EHH3jZNJIYAADAO19nWJKtW7fu9ttvZ1mWPss0ceJE1zIAAADgixbMNyxrbGz8r//6L5PJRPttdejQ4cMPPwx4zQAAAKJeMxelRVH01NKdPHmyVqu12+0MwwiC4PapYgAAAPDCp57SrvM30J+nTJlis9kYhmEYJjU1tb6+3u3qAAAA4FYzF6Wbffro5MmTubm58kRMPXv2bGpqCnAdAQAAopQ/94ZdI7m8vFwe9rJLly47d+4MRN0AAACinD8x7NY777zTsWNHQgjHcSaT6dVXX3UqgPmJAQAAnLQ4hr1M7XD+/PlBgwbJzeI5c+a4XQUAAAAoP1vDnhq1oig++uij7du3p08V5+XltbaCAAAA0cv/i9Ke2riiKC5fvtxoNAqCwHFcXl7e2bNnm127FUcaAAAgAElEQVQLAAAgBgWyNaz8761bt5YuXarRaAghZrN5xYoVrs87AQAAxLiAddFym6xz5syRbxX369fvn//8Z6B+HQAAQBRo7QNLzbZx6+rq7HY7TeKEhISPPvrIj98IAAAQlQLWGvZu8ODBNImNRuOxY8eC80sBAADCXJvHsNxELisro1NBCIKwcuVK3B4GAAAIUmuYWrZsmcFgoM8ydejQ4cCBAwhjAACIZUGNYUmSPv744/z8/Li4OEKIw+F45ZVXMK4WAADErGDEsFPQiqJYW1trNpsZhtFoNMOGDQtCHQAAAMJQUFvDyibvmTNnioqKCCEWiyU5OfnChQvBrAkAAEA4CF4Mu50zcfz48TzPMwzToUOHp59+OmiVAQAACAfBvjfseg94+fLlDMPQfluVlZVBrg8AAEAIBTuG3dqzZ4/D4VCpVFqtNicnp76+PtQ1AgAACIawiGFJkr799tsePXoIgsCyLCGktLRUcjdyNbpVAwBANAl9DCuTdc6cOYIgMAzDsmyvXr28lJQQxgAAEPlCH8PSj5P1jTfeSE9Pp1Mz5eTknDp1SkL0AgBAlAqLGHZVUlJCe1Dr9fo5c+bQhchgAACIMmEaw5IkrV69mg7xQQgpKytDBgMAQPQJuxhW3gB+5513EhMT9Xo9IeSee+7BEB8AABBlwi6GnYiiOHToUNp9WqfTNTQ0oFkMAABRI9xjmKqoqBAEgU5X/OCDDzolMYIZAAAiVGTEsCRJDQ0NNpuN4ziGYVJTUw8cOBDqGgEAALRWuMewsqX797//vbS01Gg0Go1Gi8Xy61//Gu1gAACIaGEaw15Gy1q2bJnRaGRZVqvVDho0yO2KAAAAESFMY9i7Dz/8sLCwMD4+nmXZ7OzsDz74gC5HBgMAQGQJ0xj2Pna0KIrXrl0bO3aswWDQarV2u33VqlVO6wIAAIS/sIthH0OUFnv22WdtNhu9QP3YY481NTUhgwEAIIKEXQxLzSWx06v79+9PS0sjhBBCkpKSDh8+3Ma1AwAACJhwjGE/dO3aled5lmXtdvuiRYtCXR0AAACfREkMX7p0qbq62mq1ajQajuOGDBmCSZkAACD8RUkMU9u2bcvNzdVoNFqtdtSoUVeuXKHLkcQAABCeoiqGqeHDhwuCwPO83W7funWr907XAAAAIRSFMSxJ0ujRozt06EBHvszMzPzmm29CXSMAAAA3oiSGXe8Enzp1asqUKRzHEUKsVmttbW3oagcAAOBeNMSwlwmX+vfvr9Fo1Gq1wWDYsGFD0KsGAADgTTTEsFvyLeH58+fHx8cTQnier6ioCHW9AAAA/iNqY1hp165dKSkpcXFxLMvm5ubKY1BT6L0FAAChEs0x7HTDuKSkRBAEjuNsNltlZaVTGeV/0bkaAACCI2pj2CmD6b8zZsyw2+08zxsMhi+//FJyl7VIXwAACJqojWElZbLu3LkzPT1dEASLxVJYWPiHP/whhBUDAIAYFxMx7OTGjRtDhw6Ni4tjGMZsNh85coQuV6Y12sQAABAE0RzDXh5kkiTpmWeeSUpKEgRBp9MtXbrUUzEAAIC2E80xLBNF0amlS/97+PDh0tJSm82m1WoLCgrq6+vlAqGpKAAAxJiYiGHvhg4d2r59e41Gk56efuLEiVBXBwAAYghiWJIkacOGDenp6TqdzmAwTJkyRUKDGAAAgiLmYtjTE0pffvllly5d9Hq9IAg/+clPDh48KLk8QIzniQEAILBiLoa9GzZsmNFoZBiGZdmpU6e6FkAGAwBAAMVcDDt113J6SZKkF154QRAEhmEIIeXl5W7LAAAABETMxTDlJU1FUTx8+LDZbCaEEEI6derU2NjY7FoAAAB+iMUY9uUW7zfffNO9e3edTsfzPCFkzZo1waodAADEkJiLYS+TN7gG88qVKxMTE2mz+Mknn/z73/8etHoCAEAsiLkYllrS81kUxU8++aR9+/a001ZxcTE6SwMAQADFYgy3lCiK/fv35ziOZdkuXbps27YNMQwAAAGBGG6GnLjjxo1LSkrSarVqtbqqqgpJDAAArYcY9gkN3UOHDtntdoPBwHFcTk7O2bNn3RYDAADwEWLYV3LEjhkzhuM4QkhKSor8LBMAAIAfEMM+cerVtWHDhtzcXEKIwWAYPny4p8IAAADeIYZbQJmvH374YVpamtVq5Xk+JSXlyJEjIawYAABEKMRw89w+Xkz/nTdvnsVi4TjOYDDs37/fy1oAAACuEMOtIopiQ0ODw+HgeT43N3fatGlNTU2hrhQAAEQMxHAA7N27NzU1lfbbuv3220+ePOmppLKJjOYyAAAghv3kGqJjx441mUyEEIvF8vOf/zwktQIAgMiCGG4VpzBeuXJlRUWF1WolhBQWFn799dctWh0AAGINYjgAnNJ0+vTpGo2GPs60a9cuH9cCAIAYhBhuLbdp+thjjxkMBo1Go9frN2/eHPxaAQBAREAM+8nTJInyD5s2bXI4HAzD6PX6Bx544ObNm65rAQBAjEMMt6HGxsbMzEyLxSIIgtVqdepBjUgGAADEcJubMGGCIAgajcZut+/YsSPU1QEAgDCCGG4rysZuQ0ODXq83Go0sy/bv3//69eshrBgAAIQPxHDbksP49OnTGRkZhBBCiNlsnjNnjoTr0gAAMQ8x3IaUo0/Tf0tLS1UqFcMwhJAJEyY4lZQQzAAAMQYx3LZcO1Q/8cQTOp3OYDBkZmaWlZV99dVXoaobAACEHGI48FxbtMoGsSRJy5cvLyoqMplMer3ebDavXbsWY00DAMQmxHCwySn70EMPmc1meoG6oKAASQwAEIMQw4F369YtyUOUOjWLJ06cmJub265dO57nu3Xr9sMPPyCAAQBiCmI4xA4fPlxYWMhxHMuyaWlpe/bsCXWNAAAgeBDDYaGiokKtVtPHmcaNGyfhujQAQGxADIeYHLfr1683Go2EEJVKVVFR4fQqAABEJcRwGDl16tTdd99NCFGr1YmJiadOnZJ+nMRIZQCAKIMYDjtjxoyhV6dvu+22RYsWhbo6AADQhhDD4ejXv/61xWLhOE6r1Y4YMSLU1QEAgLaCGA5Tn3/+eUFBAcdxOp0uKyuLXqAGAIAogxgOC54eMh4zZoxardbpdBMmTDh9+nTwKwYAAG0KMRx63ud1WLNmTXZ2tsViSUxMHDNmTFBrBgAAbQwxHAGOHj3auXNnnU7HsmxBQcG3336rfNVT92l0qwYACH+I4TDlGqILFiyw2WxarTY5OXnNmjUSpkcEAIh8iOEIIKfsli1bOI4jhDAM88ADDyhfdf0XAADCH2I4Msj5um/fvm7duul0OkJIdXW1axkAAIggiOHw5SVW77vvPtomNplMc+fOdR1pC5EMABAREMNhzUuaPvvss3S6Yq1WO3DgwJs3byJ6AQAiDmI4THnPVPrqxYsXp06dSke+tFgsr776qvJVpDIAQPhDDIcvH3P0kUcesVgsgiCwLDtt2rS2rhUAAAQQYjhSKUO6oaEhOztbo9FotdouXbpcu3YthBUDAL95+fK9bt26WbNmvfvuu1euXPFeEiILYjiyKQ/F/v37azQai8WSlZXlNPKlKIo4aAEiguuhet9995nNZnr7iWVZvV4/b948X1aEiIAYjmCu94AnTZpkNpvVarVer6+pqXFNXxyoABFBPlRzc3NpAOv1eoZh6M95eXk4tKMGYjiyuT6qVFdX53A4tFoty7LDhw8/d+6c97UAIGylpKSQf2MYJjExsWPHjoQQrVb79ttv40CODojhyON67DktaWpqeuCBB3Q6XVxcHCHkN7/5jacVASB8OB2h/fv3l5u/Dodj0aJFkiT94he/YBiGYZjy8nLvq0OkQAxHFeVl6pqaGp1Od/vttyckJDz00EM4RAHCltP48PTfxMRE2ghOTk6WL2stXbqUBnNVVZXr6hCJEMOR59atW5LnNrHy3/r6+qSkJHrQPvzww8piABCe6BH6m9/8hmYwz/NvvfWWvHzt2rV0+QcffBDiikKAIIajh9t8/dOf/pSfn6/RaAghJpOJTs0EAOFMFMWvvvqKHra5ubnKlyZPnky/WO/du1cuHIIqQuAghqOfKIplZWUGg8FoNOp0uj59+oS6RgDQvH79+hFCJk2apFxYXFxMH1u6evUqXYIYDgnX7rF+QwzHij179uTl5dHv0cXFxZcvXw51jQDgR5weQbx+/fpDDz2kfEmSpOzsbPrAUkhqCEqBGjYYMRwT6I7y6aefduzYkc5YbLVat2/f7loGAMJZ7969CSFTp04NYGsMAsLvvwJiOOYMGjSIZVmWZbVa7fDhw+lCHMYAodXsMSiKYt++fekjTLt27fJlFQiOTZs27dmzR/6vPG6Sj38gxHBMcPri3NDQYLfb6QXqsrKyf/zjH5LLHoMjHCCEXBu7mzdvlofySExMXLlyZVNTU+gqCP8yevRo+kcZMGCAcrnvp1DEcAxRPpvY2NjYuXPnuLg4QRDS09M//vhj5C5AuFEeld26daOPKslhnJGR8cYbb4SweiBJ0qxZs+Q/ytWrV/04kSKGY4jr9+tHHnlEp9OpVCqLxbJ06VIJjWCAUHC6jOl0qP7zn/8sKCggP0ZP/YIgvPDCCyGrN0jSiRMn6F+E53l5IS5KQwusXbvW4XCo1WpCyKBBg27evIkkBggh16/LOTk5ykZwu3btsrOzBUGg/x04cGDoKhvT6F/n4MGD8p/m4MGDUssbM4jhWCeK4gcffJCRkZGTkyMIQl5e3tmzZ6WAPhUHAK1hMpnoWV6tVi9ZsoQuPHLkCMuyDMMUFhaGtnoxbtu2bRqNhmEYjUbzxRdf+LEFxHCMcrpmcurUqS5dumg0Go7j0tPTFy9e7GkVT/8FgDby+uuvp6SkjBo1Srlw7969NJvNZrOE4zF0nn/+eXqtQqvVfvrpp64NmGb/NIhh+I+qqiqr1arRaARB6N69+0cffSS/5OnGFQAEgevc4XLPILvdHqpagSiKtbW19Fa9yWSSF0otOU8ihmOX284gv//97+kwPTqdzm6307nVvKwOAG3K6QiV/9urVy/aGs7JyQlR1UCSJGn69On0D9GjRw/XV305TyKGY5rT9Gryz5WVlfS2k16vX7BgARIXICQ8HXr/+Mc/rFarwWCgg07jCA0++TPv3bs3nQG6W7duTi+5/a8rxHCs89QVa/78+Tqdjud5lmXz8vLk6VwAIOSmTp2q1WrptdBTp06Fujoxip4whw4dSlvD/fr18+/7EGIY/sX1G9xXX33VpUsXQRAYhrHZbGvXrvVSHgCCY8yYMfJzw3379g11dWKaKIr0Lh4hZPr06f5tBDEM/+H2GnV5eTmd95Tn+YkTJ4aoagAgSZI0b948+SnV9PT0UFcHJLPZTMdR8Xs2d8RwWAjzluWiRYsYhuF5nuf5zMzM/fv3K191G94AEHCzZs3ieZ5msCAI69atC3WNYt3hw4cJIRaLxeFwXLlyxb+NIIbDRbhlmFM/6gMHDmRmZsbFxWk0Go1G43qBOtzqDxAdrly58uWXX65Zs4bOF06vRZvN5qqqKmUxHIAh8fjjj9NhVVoziApiOCyE1SHkpZvfT3/6U3oW4Hl+5syZbssDQECsWLHCaQRp+m9aWtqhQ4ckXIgKA4MGDSKEJCUlteYmPWI4XNy6dSvUVWgGPdSfe+45OsQHz/P5+fk3b95Uvur6MwD4LSMjgxASHx9PwzguLm7w4MHff/+9a0kcdEFGP3B5ZO+amhq/N4UYDr0wPH68Z+p7772XmZlJv5inp6evX78eo2sBtJLbw+fGjRupqakqlYpl2blz59IAdi2JQy/4RFGkcyvR0aT9vjEsIYbDSlhdYvL+BPr169f79OkjCAJ9sLi4uJheJQOA1nDbzeLMmTPyq97XbatqgTtyr/WOHTu2ZjuIYfgRL+nr+i1h/vz5FovFYrEQQtq3b3/kyJGg1RMgmrgdWdZ7Yae1kMHBl5ubS1vDP/nJT1qzHcRwuJCPoj//+c+hrYlbng7yPXv23HnnnXSID7vdvnTpUpwOAPzg6cDBARWeGhsbtVotx3EMw8ybN681m0IMh5e0tDSNRpOXl7dgwYJQ16UFhgwZIt8jqa6uDnV1ACJVAEMXuR5wyo+uvr6eEMKybFFRkeTzp+r20gViuE34cZmIFpbHiS0oKIigjhi3bt2qqalp3769TqfTarW5ubnHjh3zZcWwfUcAbSoIe/7p06fr6+uPHj26Zs2abdu21dXVnT17tq6ubvPmzQcPHpw2bdrOnTudKoPj0S23H8sTTzxBBzW6evVqK7eJGA4GHztW7Nu3T6VS0R7IQ4cOdXo1/I+Q+vp6eYif+Pj4Znvw454WgOsB3tL5eSRJ+uGHHyRJunLlysqVKwcOHJiXlycIAsuyLMsSBToqrfJZ5OHDh0fQGSZ8iKKYkpLCsqxOp2vRecxtMcRwm1i7du0f/vCHlq71y1/+UqVS0SQuKChwLRD+x8mhQ4d69+4tD7bXu3fvr7/+Wn41gtr3ACHk5bhQjuNhsViKi4vbtWtHR9QhLnie5zjOdTldnRBiMpm+//57HIbNcvqIVqxYQa9cJicnSy4tipZ+nojhwLvzzjvpLj5ixIgWfUWi83jTI2Tq1KltXM02tH79ejrcOcMwFovljTfeCHWNAMKCl77QTi/duHGDjt3hFKvKFq0cyTQSlMuNRqPNZktJSSktLe3Tp09RUVFBQUFycrKyDMMwmE28WW7/ZEVFRRzHqVSqPn36OL3kx+eJGA48eUfPyspq0YopKSkMw9DrSLNmzWqj6rUpeRd85513brvtNvo5JCQkPP30026LAcQgt08Gr1mzZtq0aUVFRfn5+SaTybUJq2zFyj/I/zUYDHa7vbCwsLS0lM4O7vYo++tf/7p3795p06aVlJSsWrXq6NGjQXi/kcvtZ/j73/9ep9MRQliWXb16tZeSSnTAQbdpjRgOvHbt2tGD5MEHH/R9reeff16r1Wo0Gjo6mtwajtwbqKIolpeX8zxPP42OHTtu2bJFisz3AhAQ8s5/8eLFioqKtLS0oUOHGo1G5aVmT+nLcZwgCEajMS0trV+/fuXl5dOnT1+yZEl9ff2XX37p2mjz1Npu9pSCI1TJ9XOjc2xQY8eO3bp167Zt2z777LNPP/10586dzz777IwZM2bPnr179+5nnnmmtrZ28ODBOp1Or9fTKxllZWXoKd22RFGkX5QIIbfddpsv5SVJampqslqtLMvSGzkajeb1119v+8oGw4IFC+x2O31fHMf5PSUnQBS4cOHCxo0bCwoKvLR0ZRaLJTMzs7CwcOzYsQcOHNi5c+f7779//fp1eWstzUu35RG6zVJ+RHV1da493egPTss9XcbYuHGj0/YRw63idg+W+0rk5OT4uJ358+fLGUx/eP/99z1tP+IcP368W7duer2e9u/38bZ3dLx3ALkVVVxcLJ+OtVot7VpFv54SQoxG48CBA++5556lS5fu27evqakJhwDV7OcgiuLEiRPvueee/v37t+mv3rlzp6egdZu7arVabpVRlZWVrr8FMew/t73jTp06Jd/f9fGitCiKd999N/3LsSyrUqn0ev2pU6ei6UECURTHjRvXvn17jUaj0+n69OlDH7HAGLkQxZyvPf6YIAi5ubkDBw6sr693XSvGd37fxx7ZsGGDsq25aNGiNhoC5eWXX46Li1P+BbVarclkstlsmZmZxcXFQ4cOHTNmzJw5c5YsWTJ//nz6w40bN44ePfqb3/yme/fu8p14URRxbzgAPP2l9+7dK/+RZs+e7cumTp06xXGcw+HQarXycwg3btzw8TdGClEUZ86cmZiYSGeD6NKli9OrruWDWDuAAHPdgR0OBz0z8Dw/atSov/3tb26LgY8qKyud2pqEkLvuuquNft2sWbPkxlJ+fv7+/fsln78zKdtUroURw63i2i1i2bJl8g6xdu1aXzZSXl5uNBqNRqN8ecpisdy8eVP+A0dos9htDxFRFEtKStRqtVarzcnJOXXqlGsB13UBIo7rPnzx4sXFixdXVVV98803ktdDG/s/5elsMHfu3Pbt2zv1GzcYDIQQp+/3gVVWVlZUVCR33PHlYp4v9+MRwwE2cuRIeed49dVXmy1/8uRJ2gjmeV6r1apUKkJIenq6U7GIPixdv6w8//zz7du3Z1nWbrf37Nnz3LlzoasdQOD5d8BG9GHeRpzCbPr06bTFQhst8smW53mr1er2zmsAq+Hpv80u914AMRww9POl153ozvHCCy8oX3ItLEnSnDlz6Pc4u91OH1gihOTl5QWz5m3E6fKL0xf/y5cvd+/e3Wg0GgwGo9HYdscPQAi5XoT0+zmiWODp03jhhRd++tOf2mw28u+BR8xmM8uyRqPRbrenp6fX1dVJbfPptTRxvT8t5hZiOJA+//xz5XA2W7du9V5eFMXCwkL6ZG12dnZWVhaN4ZaO+xGGfHwqcdSoUXq9nud5tVpdWFjo3yDpAJGipbcSY5DTe1+xYkVOTo7y7q/FYtFoNBzH5ebm0vQNeSVb+SpiuLWUn+m0adOU9ypOnDjhfcVr165ZLBaTyaTX60tLS8eOHUtTfODAgW63H1l8POOsW7dOr9fTz23AgAHff/99UGoH0Ib8u9eLBrGsqalp1qxZJpOJzlGhjGGGYUpKSpTPTweBH21cL9txghgOpJSUFEIIvXVhNBqPHDnivXz37t3pjqXRaHbv3r1gwQL6X2UMRyWnffF///d/8/Pz6QGWnJy8atWqUFUMIOR86dTjaUVRFGtrax0OR1FRUU1NzcWLF9ugggHm+tYeffRRuVe5yWQymUzyIySFhYXbtm0LST3bDmLYT667zrJly5STnMTFxdH+kK6ryD/Qiy30irQkSevWraP/HTZsWNu/g7Cg/BjLy8t1Op0gCDzP9+7d27UAQHTz41Kn08KDBw8qG47JycnPPPOMsmSQG9zen/JwWrhjx47Bgwfr9Xra/FUOK2axWEaNGrVp06aoPCEghgOmpKREud+YTCY6lrcT5W50/Phxi8UiCAIdin3JkiX03vD06dODVu3g83Jhp76+Xj4IU1JSvF/VB4gmPj7f4qUA/TcxMZE+cCHr27dvW1XaN67PXjo5dOhQbm6u8gEkq9XK87zFYklLS5szZ47kkujRlMeI4QCgd3mtVqvyxnBiYqLkw/Fz7Nix+fPn059XrFhB29PTpk0LTs2Dz/sHIoriX/7yl06dOqlUKkEQDAbDsWPHlK9G07EHIFPu2CdPnqysrMzJycnIyMjOzn777bclD9mj/O+xY8e+++47SZKWL1/ep0+fGTNmJCYmEkJYlmUYJjc31+keWTAPJS9fHZYvX56Wlka/ecsdoenTR48++uihQ4dczxjRdxJADAfGz372M3k8F7rfWywWZQHvV4TokqeeeooQolKpHn744WBVPIwoP5bKysp27dqZTCar1VpRUYEe1BD16P7fo0cP+hyO3JY1m83ffvut5PkcIori448/Tk8d/fr1U75UW1urVqtpF8iUlJQgvyPq1q1bcj2Vy1988cX+/fsTQjiOM5lMBoOBXgvMzs52OwFMtGawhBgOFKvVqryiYjQaTSYTHTbZLbc7U3l5Od3CiBEj2rKyYcftDaTnn3/eZDJptVqdTmc0Gul1e4Aolp6eLqcvHVCPGjlypGth+WBZunSpMrOlHx9Hy5cvl18tLy8PzhvxVFVJkr788svS0lJ5MiK9Xt+uXTuO4xISEvLz8+nsQy19VDfSIYYDYMmSJfKO7nA46HdPvV5/7do1ZTFPN0jk5YMGDaKH3/333x/M+gdTsz3+na6z3XPPPSqVin6zeeWVV4JRRYCg++KLL7p27Srf0mIYJjU1Ve4tbDabL126JHnIoezsbFqM5/ldu3a5lqmtrZWf+Tl27Jj3blNtZ9u2bd27dzeZTPLZUm66pKSkHDx4UFk4WhPXLcRwq4ii+Pnnn2dkZNCdqUOHDm+//XZSUpLdbtfpdPL0DD7uUoMHD6bb8WUUzMjly1lA+dLEiRMNBoNOp+N5/qmnnmrz+gEEXVFRkRxOiYmJK1eulCRp/vz59CZX586dPd1effnllwVBoJE2ePBgebn044OoR48edONPPPFEUN7Qj+zdu7dz587yG2RZ1mq1chyn1+t/9rOfuc6/6+UUEZXxjBhuFVEUlcfP4MGDz5w5Y7fbGYbxYySsIUOG0HHali5d6vZ3BaLKEWnRokX0bllaWlpxcfHhw4d9WSuWPzEIZ0575tWrV+Pi4mjT0Gazye3CyZMn0xPLokWLPG2quLhYPv80NDR4+hUbN26kZWpqagL6VtyTf/u8efNYlpXb4vT8xnFcZmbm5MmTP/vsM9eqxiDEsP/kvWfAgAF0J6M9KWhfLU9fYL0oLy83GAwcxw0ZMkT5K0J1ESlM0C4eFy5cKC8vz87OdjgcycnJtbW13q9vx+ZnBZHod7/7nRyldM4xuvd26tSJZvOKFSs8rTtjxgwab95nFlq1ahXd/v/8z/+0tHotOrLoqzdu3Bg3bpxy9CuLxcLzvEqluuuuuzzNqxazEMN+ctpvpk2b9uGHH9Kf77rrLhrDLd1mdXU1vb6UlJTk+itimfxRbNy4MT09PSsry2AwVFRU0O89TmWafUgMIIScOjyLonjgwAEapUVFRfJLly9f1mg09CJQQ0OD271aFEV6R4xl2QkTJkgeUk0UxYqKCoZhNBrNpk2bWlpJTwXcVunjjz/u2bOn0WiU7/vabDaWZS0WS2lpqdMw+zhUKcRwADjtQPQ5dLvd7qmAJ7NmzaL7rlardereFbNcP7qDBw/SBw3pU2Hnz5/3fV2A8NS9e3d55DhK7imSk5Pj5blbtVpNO4SuX7/eyyO28uBCjY2NflTPl7zcsmVLcnKyfPGZZdl27drpdLrk5ORp06Z9/fXXXh648qNK0QQxHHj0bo3BYGjpnbLCpjMAACAASURBVA/6pZgQYjKZlMNWxDjXI/aTTz6hvUNZlk1JSaHjG/i4BYCQ89LWlBfKHT937drltoAkSZ999hmdny0+Pr6+vt61AHXgwAGNRsMwTIseHW728pL884wZM5KSkgghdPQujuN4ns/MzHzggQdmz54tzyYeax2vfIcYDrw+ffqwLMtxnNzh2fedjD6cQwiJnWGl/VZVVRUfH8+ybHJyspfhP2P8CIfw5D2DX3nlFXoeMJvNXhqO8qOSer1+w4YNnrbfu3dvujXaAdu/err+8NZbb/Xo0cNsNsstYPqsc0ZGhus8abgH7AVi2H+edqnhw4fzPC8IgjxKpe/ofux0lwgo1/PRa6+9RseeZVk2KSkpuh/0gijgS0Pw8uXLt912G8226upqp1eVg1JVVlbSfI2Li1u/fr3TNum/f/7znwVB4DguMTHR7yx0WmXr1q3Dhw8nP8YwzKJFi86ePetpRS/fJ2L8RIcYDrzRo0fT/ZJ2mmiRO++8kxCSl5cnL4nxHbRZX331Vc+ePemtYp1Od++992LGYogIng7tiRMn0hOI1Wr1voVDhw7RwYJcv/TLG5efGC4rK2tlhb/99tspU6Z06tSJ/kZ6/ZllWY1Gk5aWNnv27FZuP2bPdYjhwJOnCvGjw/PRo0e//vrrNqta1Fq8eHF+fj49NaSkpDh9JZdi+AiHMOd0sfcvf/kLfYY4MzPTtYzTz9euXTMYDMrrZ06effZZ+qogCLSrin+uXLkye/ZseZwQ2i1DEASTybRkyZILFy74veUo5vu1B8Rw4NGJTaiWjoSMtGgp+RPbsmWLXq8XBEGlUlmt1nfffddTSYAw4XrDtaqqiubcunXr3JZ0+jk9PZ1OSUQIOXfunPKlt99+mwYnIeTxxx9vtl+Y219x4sSJkSNHytuRJ7CxWq3jx493/b4L0r8/vW+//dbHcw5iOPDoI3r0a6MvfSIQD60kf4DffPPNkCFDtFqtSqXS6/VTp051KiDh04ZQ83Jb9LnnnqOtW0LIiRMnfNlXa2pqyL/ngRg9erS8/K233jKbzfREVFBQ4PZXe/fGG2/07t2b4zi6cY7jLBYLvQ89ZcoUT28HqBZ9LIjhNpGQkECPpcWLF/tS3tMTdeCHqqqqdu3a0cEK+vfvLy/HBwsh53YnbGxsfOihh+gIelqtlp46tFptdnY2HT/L064riuK5c+fk5KbzCm/durW6ulq+IGez2ei0EE4revpuevPmzRUrVshPAFNxcXEJCQl5eXn0hIZDyQs/vvQjhtvEmjVrsrKy6IA1zf4lsE/7wfuHVldXZ7fbtVoty7KdOnW6ceMGemZCeOrVq5ccvW5NmjTJdS3lDjx79mzaYJXvE8vrmkymDz74wHsFlJsaPnx4YmIivcRNn0jW6XRWq3XMmDFOA2C5rgtKLQpjxHAb8mUfxfXS1vDyiV26dOnee++lYwzZ7fbFixdj0AAIN6mpqcoHfugPgiDIP9NhmU+cOCF5uJpN/x06dKhareY4jgYnIUStVsfHxy9btszt73Xa1KefflpZWZmUlETH32BZls7znZiYOGHChKtXr7pdHYePK/8+GcRw4LXydI+d20duv8E4fXrTp0+32WxarZbnebdzpwMEmbyLlpeXOzVeCSHFxcUnT56sr6+/++675YWdOnVqdoPTp09PT083Go0cx9nt9n79+tHw9r7iW2+91a1bN9r8lWd50mg0DofjySefRNwGBFrDEQZ7fMC9/PLLqamper2eZdm77rrLaXZxgJDYvHkzUTz8Qx98Vw4YICkGySKE9OzZ03Ujbof+cLvcda05c+Y4HA55+3q9vqioKCsrKzs7e+3atW43grOTL/z4lBDDgeFluFQfV2xlGaDcflYnTpzIzs62WCx6vd5gMIwcOdKX8xRAwMm71ooVK+Rr0Xq9nk7Bq5wxjMrPz5fTWvJwBcj7L3Lyt7/9bdSoUXa7nV5/luuQnZ29bNmyjz/+uFVvD/yCGG5G6/f7Zgu0MonR+ciJp09g9OjRJpNJEASdTnf//fd/9NFHXp6hBGhT165ds9lschAmJydv377ddd87e/bswoULExIS3F7Fcfvt31OT4ODBg6NHj6bzLhBCaL8wnucTEhIGDBggzwHs1IkaggAxHACtCcIWddFqUWzgWHL9BGpray0WC8uyer3eYrFs27YtJBWDGEf3zIcffjgxMdHhcNx7773//Oc/lS8pSzZ7g7bZq8cvv/wynQGJtqpVKpVKpUpISEhMTJw4ceKZM2e8bAqCADHcPO+jz2zevHnv3r01NTU///nP77nnnqFDhz7++OPTp0+fPn36iy+++Mc//tHt4JTNZic6RwSEa8vg0KFDKSkpGo1Go9FwHPerX/0qdLWDWOTpm3eLvk83u5D+vHjxYnnCRDoHMM/zvXr1GjFixB//+Ef5JIMraqGFGG6ZyZMn33fffTt27Fi1alVJSUlycjKdvcTpkQPlf/V6vdVqHTp0aPv27aurqydOnDhu3Ljq6uqf/vSniYmJOTk5RqMxIyMjLy8vOzt71qxZBw8evHjxYl1d3fTp02tra+fMmbNy5crt27dv3rz55MmTly9f/vzzz+X6yAfMhQsXcPAoef80Bg0aROdlMplMvXr1On/+vC9rAQRK68PYy7569uzZSZMmdejQgXZ7pg9BCYJgsVgKCwv/3//7f75sH4IGMdwC06ZNc/d4PSGE0Ns8tMej/LQfy7KJiYnywJauCe1KHruVTt4pj+BKlxgMBr1ebzabHQ7HXXfdlZ+fn5ub26FDB3qkLV++XMLh5IHr1YXq6mqj0WixWBiGcTgcmCQRgqM1N1+b7Qq6Y8cOOgOSfJLRaDQWi2XixIkLFy784osv3G4NQgsx3AI7duywWq1yLtKeDu3ataM3eGw2W3p6enp6empqqs1mM5lM9BH4hIQEev3TbQAnJSXRkRfpfxMSEtLS0mhDjeO4uLg48u8BYym9Xk9/b3x8vGuK19bWSjF/dPl4YV8Uxffeey8jIyMuLk4QBL1e/9///d/BqyXEMP96XHq5EC2K4uuvv96tWzf5VGA0GulZJS0tbcuWLa5rxfhZIqwghn1F99qTJ0/26NFj5syZK1asWL9+/YEDB86dO+ep8IEDBxoaGiRJOnjwYF1dXXV19dixYx977LGKior169fv3r1706ZNNTU127dvr6qqmjp16gMPPFBYWJicnOxwOOx2u9Vq7dy586BBg7Kzs00mk9lsNhgMPM/Tf5XpSwexs9vtThUAqtkL1CaTiX6SRUVFeLAYgqn1HTyXLVtmt9vpJTE5g/V6/d13371///6WVgCCDzEcvpwOj7Nnz544caK+vr6mpuahhx7q0aNH586dk5OTDQaD0Wg0Go0zZsxAxy7/VFdXK8fHr66uDnWNIKZ5OpCVS06fPj1lyhSbzaa8WkZvXWVlZe3ZsyeoNYZWQAxHAKdjEinbFo4fP96tWzeVSsVxHMuynTt3PnXqFB4Gg1BxPd7lH/bu3duzZ0+avgzD0P4NarU6MTFx5MiRn3zyCR1LCyIFYjiseY9e71+WERW+kz+r8vJy2s9OpVLpdLolS5b4siI+amg9Xw7eLVu2ZGVlMQxD7/taLBY6HE1ycvKkSZP+7//+r9ktQBhCDEcG3ztu4PDzj/y5TZgwQZ4vnWGYyZMney8P0HrK73Nud63FixcnJibqdDq5O6dWq42Li+vZsyedUNVpU96XQFhBDIcv3wfVwmEWWLt27crIyLBarXTK1WnTprkths8f2g7dqa5fvz5hwgSTySS3gOljjcnJySNHjjx+/Lin1W/duiVhz4wQiOEw1crjB4efH5w+tEcffZT2oGYYpqio6J133glVxSAGrV27tlu3bjabTaPR0AA2GAwJCQlFRUVVVVXfffedj4Nc4lQQ/hDDYc2/QwiHn++8f1ZvvfVWSkqKxWKhE6qPHTs2uLWD2EL3w9WrV2dkZMhtX/oDz/NDhgx57733vD893OzFbQhDiOFI5fYBfFwmDbjLly/37dtXEASj0UgISUlJuXTpUqgrBVHo5s2bNTU18sRHNIM5jktKSurWrdvGjRtbtDWcASIIYjhgfB+B3Y8toFN0aC1cuFAe4sNisRw7dizUNQpH2A/9c/z48YqKCr1eTyf+ksfL69Chw7hx4+QZkPDxRivEcAC0/vBAKzb8bd++PTU1lTZWCCHPPvusa5lYuxjYoi+OoEQ/n/fff79nz56CINAH1ukYMgaDoaio6JVXXnG7CkQfxLD/mh2y2I+t+bEitBHXP8S5c+eKi4vlflvp6emx/MfysYtQjPP0KTU0NKSkpLAsK0/fYrFYOnXq1Lt37x07drhuwfVniBqIYT95OTa2bNnSsWPH5OTkvn37NjY2+rdNJ6tWrdq8eTOeCAwaLx9sRUWF3H0mNzf36NGjnspH/V8HCdEs149l3bp1GRkZarVa+QTwqFGjfvnLX3paERcYohtiuFVcD4ypU6fGxcXJB1haWlqLNuI2aAcMGEC3VlxcfOLECU8lIbCUneCcPu1du3bdcccddDRBQRCmTp2qXMu1fHTDkJ/e0c/h0KFDP/vZz+SbGikpKUaj0Wq1duvWbdGiRU49nPH9JqYghltLeZDMmDFDObsw/fe1117ze5tffPGFctB2QojNZkOXjTDRu3dvuTtrYWHhtm3b6PLY/LvI79rtrPKxiX4me/fuHTBggEajkWcTJ4Q4HI7evXsfOXIEd6MAMdxa8sGzfv16+TEDlmXlJJ47d26LNrhy5cq0tLSRI0deuHDh5MmTxEVOTo4Uk62u4HM7UKhy4fjx4+Pj4+kw1FqtdvPmzcGuYqg5fSZ0ytuDBw9iz5Qk6aWXXurVqxc9bOlchBqNxmKxtPScgA8zuiGGA6Znz570MQNBECoqKp588kmaxKmpqS3ajs1mo8ftqFGjJEmi04gOHjy4oaEhJyeHRvuBAwfk8jhE25SXxgpd8t577yUmJtI/mdlsnjRpUrCrGDYWL15MP4cpU6bIC2Nz/1y4cKHZbJYvYtHTQlJS0rBhw86ePetUODY/IpAhhgNDvnrMMMzw4cMlSfrggw8IIUajUafT+b6dixcvqtVqup0JEyY4vbpx40b6WGFJSQkO3TAhiuLZs2fvuusu+ocTBKG0tDTUlQoGpz3wxo0b8gWb4cOHx+b+eeXKlYqKCrkvPb1GotVqBw4cuHTp0osXL4a6ghCOEMOB0a9fP3oCSk9Pp0u2bNkiCALDMDabzfftTJkyRb7duH//frpQeUarqKigXSvp0O0QWspLsiNGjLBYLCaTSa1Wp6enb9myJeqjSPkG9+/fL8dwXFxcCGvVplyvjoiieOPGjdra2qysLPm7OMdx8fHxSUlJ2dnZu3fvDl19IQIghv2kPAEdP35cPgHRYYdFUXzsscfokvz8fN9Px+np6XSt7Oxsyd3Vqnfeece/W87QRpR/o+rq6uTkZJZlU1NTCSEDBw50WzjK4pm+nfLycjmE5NkhI/GdtvR56NWrV2dlZcn9QlQqldFoHDZs2GOPPdbmdYWogBj2n3w07tixg/bJSklJ+f777+nCESNGGAwGrVa7bt0637dGBy52veys/DkjI4Nl2Z49ewbqjYB/3J6pjx49WlBQoNFoHA6HXq8vKyt7//33g1+3oJFDi44ARQi58847b968KUVyBntaovz5woULc+fOlaem1mg0arVaq9UmJiY2NDQ4rRKJHwUEDWI4AMaOHUsPxbKyMnlheno6wzBardb3mQAaGxvpXaW4uLj6+npPxYYMGUIIad++vYTDO0SaHayjtLRUr9fzPC8Iwh133KG8LBkdfzKnd1FTUyNfEIr07uLNPrO7Y8eOSZMmmc1meteJvmutVltUVLRp06ZmtwngBDEcAPTGMMMwhw8flhfS5/QTExN9386CBQvoRS2TyXTt2jWnV+UjeeHChfTgxwQDIeT2WSalHTt2WK1WvV6vVqsTEhK6d+9++fJlT4UjkfJdyBk8bNiwGzduRO4b9DJ2lSiKb7zxxu23307fKc/zPM9rNBqe5/Pz812/fKAdDD5CDLcKPcZef/11i8WivEp8/vx5lUpF7w76fhwuWrSIrpWRkeFlrYaGBhrD+/btQ0et4PP9ruFHH33Uo0cPm82m1WpVKpXD4airq4u+83JjY6McwydPngx1dQLA9W9UU1OTlJQkv016AFosllGjRnkZrqTZ72oAEmK4NbwcVG+//TY9XGlHKh8Pv1/96lc6nY5hmKSkJC/FNm/eTDe+fPnyltYZ2pprT9rx48fbbDaDwcBxnCAI48ePD13t2sTQoUPpDpmVldXU1BRNYXPp0qXS0lL6lCCdBIneM+rUqdPixYubmppCXUGIBojhNtGnTx/61OCOHTuaPSvJBaZPn05PZ7m5uU4vKW3atIkWmzZtWmCrDW1k0aJFOp2O3kqMj4/v0qVLXV2d25LhlmHXr18/f/6864gTSvI4yQsXLgxaxXzn9MXIx0/43XffLS0tlZu/dChKvV5fUlKyffv2NqwuxB7EsP88Hd7nzp2jPa1oLyofNyJJ0sSJE+kxX1RUJHk+X2zYsIGeFyorK1v5FiBoXnvttezsbI7j1Go1x3Eajaa0tNRt9z3l3z3INx2Uu/Sbb76ZlpYm51BSUtLEiRNdV9m3bx8tkJycHP7DU/gyZcKWLVu6du2qVqvlIWk5jktOTi4rK/vqq6+8rAjgH8Swnzzd9RFFcdq0afTEtGzZshZtauzYsXRF+XlTt2eNmpoaenaoqqrCGSGCiKI4YsSI9u3bq1QqhmHUanVKSsqePXu8lJdCcdIXRXHcuHF0FFX5PiglT18hk/fGiRMn0ueUwo33D1B+9caNG5MnT6Z38eW3TGeVPn78eLPbAfAbYjjAnn/+eTqooVarlXw4dJWn2traWkJIQkICjWFPoxnT0fPlcyLODhFEFMU1a9ZYLBaj0Wiz2Xiet9lsGzdulMLp7zh69Gi6g3Ecx7IsHZiC3mSRB4mjbty40bdvX0JIamrqt99+G6oKe+G9kxT977Fjxx5++GGGYZRfOAghhYWFq1evFkXR7Vrh8/eCSIcY9pPbI5MGJO3HodFo5NEofTRu3Dh6/N93331ebmgZDAaGYSwWizzjIUSWTz/9ND8/X6vVdujQITk52Wq1/vznP3cqE5JzvSiKTzzxhJxDDoejoaFBFMX333//jjvuIISo1eo333xTLn/9+vWZM2f27Nlz9+7dkRJLynoePny4sLDQqf9zXFxcYWHhsmXLfO8SD9AaiOGAKSkpUc5vSAgxGAyffPKJ71ug40Wbzeb77rtPuVx5zD/11FO0dVJQUBCwqkOwKP+UM2bMsFgsgiCo1Wqe53Nycq5cuRLaitF2MG0XZmZmnj59WvltwOFwcBw3ZswY5YpNTU3Xr1+/ceNGKGrdYvSNXL9+ffbs2XTAUeVVd61W+8ADD3z55ZehribEFsRwYLzzzjs6nU4eV1YO465du/q+kXnz5tEVi4uL6RLXL9333XcfbZTMnj0bX8kjhae/VG1trcPhaN++Pe2Im5SU9NJLLwW5brL33nsvLi7OarWqVKp77rnHtUDv3r05jissLJSXROIeSDtCKu/+0gAeNmzYd999JxfzdEvItQBAKyGGW0U+FHNzc+m1aFe1tbU+bmTNmjVyp1O3B/m+ffsEQSCEsCzb2NgY2PcCbcT7eXzr1q1paWk8z5tMJofDQS8FexoTse1cu3YtMTGRZpLD4fjhhx9cy4wZM4YQ4jpjWPgHkiiK586dmzFjhtzvzGq1Mgyj0Wiys7OXLVt2/vx5ZeEQVhViEGI4AF5//XW9Xk8IsdvtVqtVp9PNnTu3qqqK53mGYXieVw717n077dq1I4QkJia6PRfI0yDm5OTgZBE1du7cmZmZaTKZbDYbHUaNZdlZs2a5LRzwvzvdII1Y2jp85ZVX3JZZvXq13PcwgnzxxRcFBQUsy8rX2+mXicGDB69ZsybUtQNADLcOfaxz9uzZtJFK2e12+qp8p00QBO9jvtN/jxw5olar6aMs77zzjlMZSZLsdjv9FXTWJiRxNCkqKjIYDGazmeM4GhWe5kl0/blFXDeyYsUK5Z2USZMmuW6cPklMvyL493vbiJeLDVOnTnU4HMr+zyzLarXaF154odnVAYIGMRwAffr0kWPYZDJt2bJFfik3N5cGs9FobLbj9Pfff0/nTWMYZsGCBcqXRFGkEz8wDNOvX782eRsQdE43IJcvXy7HBh1AMScnx1PhQP32w4cP0weT5CSeN2+e25KTJ0+mO/mFCxcCUoE2cu3atcmTJ9MhdOiXYFptnU7Xo0ePXbt2ySUD8rUGoJUQwwFAn+UghKhUqjvuuEP50jfffENnPKQFfvnLXz700EMbNmxw2oJ8CujevTshhOO4zp07O5UpLi6mpxWnm804fUQo+UKI8i/42muv0fuXt912m9FopGNQf/bZZ05rBdD999/v1Jth5cqVkrvUpz3527VrF9gK+MHTh3Dq1Cn6BDB9I/RWkUajSUxMrKioUH6MLdosQJtCDLfWF198QcfUZVk2Pj5+69atyldFUTxx4kRaWpryQSZCiNwh1unIr6+vZxgmISGBZdlFixbJy3/729/SFR0OB77CRzd5TFPlgzSuE0IE5KL0J598QgiRe/hTS5cuddvyrqqqIoTcf//9/v3eQHGt282bN6dMmZKZmUnvrMsfHc/zHTp0GD58uDzFpC9bAwgyxHBrvfDCC/KR37FjR3m58vC+cOFCly5d6ERp9AQxf/58T8f/bbfdRq9ja7XaSZMm/fWvfx03bpw8wN7q1atdfwVEKE/fqOgIkTzP6/V6OYyTk5MDPlLVgAED5Au2chjTh91dB5Ch18kfffTRwNahRVxHNamsrKTj1hFCjEYj/dzi4+Pz8vI8TUHm9s5329UZwDvEcGvR7qNURUUFXeh6snj55ZcTEhJoMZvN5uWwr6ura9eunU6nIy769+/vVBinj8jlaZwsuuT06dMjRoxw2gF69eoV2L94YmIi3XL37t0TEhJo5O/du9e15NatW93eEwmV3bt39+rVS34ASRAEnufVarXRaBwzZoxy2Bzv41kChBxiOABGjBjhcDjS09NPnz7tpdjBgwenTp2al5fnOlGa06lhyJAhdOJhuSXEcVzfvn0DX3UIER+zYdWqVZmZmcoL1AcOHAhgNdatW0c3O3369OTkZPrzzp07XWs7fvx4+uq3334b2iTbunVrt27d6DMFPM/LjXiz2VxSUnLmzBm33298qTMSGkICMRwYzzzzzKZNmwJ4GG/cuLFPnz70rjPDMKWlpYHaMkQQukd17dpVbhCr1Wo6Bx/Hcenp6Z06dbrnnnsmTZrkcDjGjRunXMsXTU1NtB9T//795V8hj2GpRK9I5+Xlua1hcHz22WcZGRlOVwgYhrHb7VOmTAn/aRYB3EIMh7Vnn332ySefdDukEUQr1x7Up0+f7tKlS8+ePelcxTI5hwghBoPBS0ckL8aMGWMwGBobG++44w76vNyxY8eUlZk5c2ZKSgr9RT179gzEW2yxysrKnJwc19s0dBpgZUm0aCHiIIYDqe1OATi5xBRP3fdEUaQBzLIsbZ7KQyKfO3fO799y9OhRSZIcDodGo9FqtdeuXZMLLFy4kDaXqZSUFFrY6cJvm+6fw4YNc5qCkGXZTp06rV+/3stbwyEDkQIxHDFwWgGlefPm0UDSaDQ0GiXfpkf01D27Q4cONORef/11eTnt3q9sdpOgTHSt3Hjv3r3lCtDH+WbMmCF5frN4BgkiC2LYf76c8gLyKyB2eBmaUfkD/Xf69OmdOnWSn2JqZS+kzp0705zbvHkzLblp0ybaAcpsNiuTuKioKJh7Jp0SWP4S0NjY6OW3B+GoBAgsxHCrBO0qNE4rscZLd1+3kdzSLbsuueeee2jO/f73v6fL6YxPNP8SEhIeeeQR+QI1nRK7lTXxvZ70Cjxls9nk8bCazWOA8IcYjgA4oYArvwdT8/QNb8iQIfQq95w5c+hy2mOLht+kSZMkSaqvr6f/5Xn+zTffVG6hTffSJUuWxMfHk38P+MXz/MaNG13fDo4UiESIYYAw0qL7mgEZz1L+ee7cuTRi6YNPO3bskBugGo3mq6++osXk55gzMzOD2ROqoaEhOTlZOZWZ22m50TkLIg5iGAAkSZI2bdpE423o0KGSJN28eZM2PTUazYABA+Rib7zxBi0WFxd39uzZIFeysrKSXqCml8cLCwvll3AfByIUYhgAJFEUr1y5QoeLkcfomDFjBsMwSUlJX331lbKVWVhYSFulXbt2DX635CeffDIpKUke7dXhcFy4cAEZDJELMQwA/0KH6cjOzpaXfPbZZydPnnQqRsdRNxqNLMuuW7dOXh608Dt06FB2drbRaKRTKiUmJn7yySfyFwVkMEQWxDAA/Cu6UlJSGIYxmUyeBm6TEy47O5s2RnNzc4NXS0Udzp8/f++997Zv3552ItPpdLNmzZKC0l8MILAQwwDwL3TEZp7nL126pFyuzDb67+rVq+n0glqtds+ePVKIkm/Tpk0mk0nutNWtWzd5ehUkMUQKxDAASJIkiaLYo0cPhmF0Op0v0yQUFxfTlqjD4Qhh5r399tv02wO9QC0IwuzZs0NVGQA/IIYB4F969epFCOE47vjx482O5/X222/LzdCJEydKoWiAyg30QYMGGY1GeaivUaNGoTUMkQIxDAD/Qkdv5nl+7969vpQvKCiQk8/pOnYQOAXtqlWrsrKy5PFGevfu/eGHHwa5SgB+QAwDgCRJkiiKcserlStX+rLKpUuX5AZxVVVVW9fQCxrJFy5cKCkpkWfp1uv1br9PoKEMYQUxDAD/kpycTDN10KBBkm9xRR8gZhjmgw8+aPsKeiPXdsKECSzL0jdisVhmzpzptpjkrusZQPAhhgFAYtUmXQAAHdRJREFUkiSpsbFRbtqWlZX5vmJ9fT2deTCEnMJ1wYIFyh7U+fn5TU1Nza4IEBKIYQCQJEnavXu3fKNXHkgrgjgF6iuvvEJniKLvKCsry1MSA4QWYhgAJEmS5s2bZ7PZaGitWrWqpauHVbOSVuazzz7r0aNHXFwc7bclCMK+ffuUBZzKh9VbgNiBGAYASZIkURTXrFnTpUuX2tpaH8s7/RBCXsaUnjNnjtFopEms1+uVvc8wSSKEA8QwAPxLa2IpfGLMtSa//e1vtVotvVvMsmxxcfEnn3wSkroBuEIMA0C0cU3ir7/+ukePHnq9XhAE2jJ+8cUXQ1I3ACeIYQCIFVOnTk1NTZWH+Kirq3MtEz7NeogRiGEAiGZOsfriiy8mJyfL0xWPGjXK7Vq3bt0KSu0AEMMAEBuUedyzZ8+4uDiaxEOGDLlw4YLbYuhBDUGAGAaAWKEM1JEjR9LBtug16ldffdVLYYC2gxgGgCjn2qilP69cudJqtdIk1mq1u3fv9rI6QBtBDANADHF63PnIkSN5eXn06jTLskuXLnUqBtDWEMMAECvkZrFTyj7wwAPt2rWjkzx26NDhV7/6VYgqCLEIMQwAMcS1mUuXrFmzJiMjQ54NYuzYsaGoHcQixDAAgCSK4pkzZ4qKisxmszwv07Vr17yUD2b1IIohhgEg1ikvVi9cuJBOzcQwjNVq3bhxY1iNng3RBzEMAPCjiF28eLHFYpEvUNfU1EjIYGgziGEAiGlu7xbv3r27c+fOGo3GbDbr9frKysrLly9jRiZoC4hhAIhR3qP0zJkzAwcOTEhIoG3ijIyMpqYmpC8EHGIYAGKXp1iVl0+bNi0+Pp4mcUlJyT/+8Q8vawH4ATEMALGo2QCWf547d67NZlOr1YSQpKSko0ePelkdoKUQwwAQc3wPUVry+PHjubm5er2eZVlBEObNm9eGlYMYgxgGAGheU1PT4MGDbTYbnRCiqKiILkezGFoJMQwA4KsFCxbIg22Zzeb6+noJSQytgxgGAGiePBL1zp077XY7TWKGYUaNGiUXCGkFIVIhhgEAmuE6VWJRUZE8V7HD4bh+/bqEJAa/IIYBAPzx4IMP0qeKGYbJzc29dOlSqGsEEQkxDADQPLct3blz58bFxdFOWzabbdu2bcGvGEQ6xDAAgK9cr04fP348Pz+fEMJxnFarXbp0aehqBxEJMQwA0AJum8VlZWWCINB+W2VlZcGvFUQuxDAAQAA899xzVquVdtrq0KHDhx9+SJej3xZ4hxgGAPCfMmU///zzwsJCOuwlx3EVFRWuZVwvayOnYxxiGAAgYG7cuDFx4kSj0SjPy/TFF19Iiqx1/QFiHGIYAMB/bmP13Xffzc7O1mg0HMelp6fX1dWFqHYQARDDAACt4rZd+8033/Tq1Uun07Esq1KpJk2a5Pu6EFMQwwAAbUIUxccff9xisdAL1F26dGlqanIqEKq6QfhADAMABIxrsj7zzDPt27enPaiNRuOePXtCUjEIW4hhAIC2QlP54sWLdIgPQoggCOPHjw91vSCMIIYBAIJh6NChPM/TMLZarZs2bfJUEherYwpiGAAgSKqqqtq3b6/7/+3df1AU58EH8GfZPY7d48477g6Qu4hgMFylwOBAgKiYHgkhCg1BB4YEOkYykYYRjdWpwTY24+iEGTIxsYnBjBMTLa20mmhkMo0dE22wcbBiakqLzQ+jxkm0WhxCNMDe+8czeWbfvR8ccsct+P384Zx7z+4+t8zc955nn30eg4F2ULe3t9PteIz4doYYBgAIPX9p+uabb7JBW9OmTdu8efMEVwy0BjEMADChrl27tmDBApPJRAjR6XSYg/o2hxgGAJhQtKHc0tLidDolSaKLJP75z3/2LgO3A8QwAEBYjBqlJ06cSE9PFwSBjqDesmXLxFQMNAUxDAAQev5GXamy+fz586WlpYQQ+mBxaWmpdxmY2hDDAAAR9uSTT0qSNHPmTNosfvvttyNdI5g4iGEAgMg7ceLEvffeSxdJFEXxmWeeURVAE3mqQgwDAGjF/PnzRVGkHdR5eXnKtxDDUxViGABAQ1atWmU0GmkSW63WQ4cOsbeQxFMSYhgAQBNYyv7xj3+0Wq08z9OhWy0tLfQt5b8wZSCGAQAib2RkxKOI2PPnz7vdbrPZ7HA4eJ5fsGDBl19+6UEGT0WIYQAAbWFZ29TUxG4Vx8TEHDhwILIVg3BADAMAaBEN42PHjpWVldE5qJOSknbv3h3pekGIIYYBALSusLCQtok5jsMc1FMMYhgAYBJobGykyxVzHJeZmTk4OKh81/ueMcZzTRaIYQCAyeHgwYOpqam0g9rhcLz11lseRdD6S2LQOMQwAIDWsaZtd3d3YWEhz/McxyUkJKxdu5ZuDxDGoHGIYQAATVMlqyzLVVVVoijSDuqsrKxIVQxCAjEMADAJqMJ406ZNBoOBdlCnpaX19PQEsxdoEGIYAEDrfC6V2NvbO3fu3JiYGEKIJEkbNmxQFkAATxaIYQAA7QqQpvStoqIimsQ8z5eXlw8NDXmQxJMKYhgAYLKiQVtbW2uz2WgSS5LU0tLiQQZPHohhAIBJb+/evXa7XZIkh8NhNBpXr17tXQZNZG1CDAMATAX/+c9/srOz6WRbhJCHH37Yuwyea9IgxDAAwCQTYKaOkpISURR5njcYDMXFxR5fTxUjgzUFMQwAMPl4P0zMXj///PMmk4k2i2fPnv3Xv/7V5y6gEYhhAIBJRtW6pWsVK7377rt33nlnVFQUIcRisQS4VQwRhxgGAJh8AvQz09dDQ0Pbtm2Li4vjOI7jONpB7b07RBxiGABgEvPZO802vvbaa4mJiXRpJpvNdvr06QhUEQJCDAMATG6Bm7ZnzpyZO3cuz/M8z6empn7wwQcTVjEIBmIYAGBSCjBKy/vBpCeeeEIQBI7jBEFYtGiRB6OmNQMxDACgCWNNROWTSKMeRJbllpaW6dOnC4LA83x8fPzf/va3WzsvhBZiGABgcrt8+fJrr722c+dO+l/WzPUexjU4OJiVlUVvFTscjo6ODmRwxCGGAQAmN1EU6VPC//3vf+mWwLNlVVdX0yk+TCZTQ0ODBx3UEYUYBgDQlmDikJW5fPky+cHg4KC/3VXB3NXV5XQ66QqJ+fn53377bchqD2OEGAYAiDxZlisqKqxWa3p6+pEjR0YtzF53dHTQDOY4bmBgIJi9aH/18ePHExMT9Xq9IAhOp/PNN98c94eAW4EYBgDQBBqlhJAHH3xw1AYxK1BTU8Naw8PDw6OWV70uLy/X6XT0vA8//HCAI0CYIIYBACKM5mJCQgJN08zMzCB33L9/vyRJgiAQQkwmUzBn8bZ+/Xqz2Ux/BMydO/fKlStjqjyME2IYAEATZs+eTWM4JSXFXxlllL7//vs0gCm73X7Lp75+/brL5aLHcTqdXV1dgU8NIYQYBgDQhOTkZLoYQ05OjnL73r17f/zjH7/44ov/+9//6JahoaGamhrWhKXxmZCQMJ6zf/XVV263m91mfuaZZ5TDp/3NXA3jhxgGAIi8a9eu8TxPCNHpdNnZ2SzkVq9eTYOW4zibzVZZWZmVlaXT6Whe0tim0tPTx3pS7+eaamtreZ6nk21VV1f7LAyhhRgGAIi8999/ny6FRAiZM2cO297Z2UlTNiYmhvii0+mio6M5jrvrrrvGWQcatKWlpQ6Hg/4mSElJOXz4cDB7wS1DDAMARN5LL73EOoSVcz57PJ6CggJl25f1Qt93330dHR0mk4n+t6ioaDwVUKZpZ2dnRkaGyWQyGo3Tpk0rLi5WPgqF3A0txDAAQOQ5HA7WwF29erXq3cOHD69atSozMzM2NtZmszU0NPT29tK37rrrLhrMFRUV46yD6jZwbW2tzWajVdLr9Xv37vVZbJwnBcQwAEDksTYuIWTbtm0BZsJik0XTf++99166V1NT0zjr4H3SlStXxsbGsoo1NDQgd0MOMQwAEGFff/218nbv66+/7l3GX+szOzub7qUaUTVW/o7f1dWVnp4uSRI9i3L4GIQEYhgAIML27dunag0Hv29mZibd6/HHHw9T9fr7+/Py8uhZeJ6/7777Aix17P1foPxdFsQwAECE1dXVKVvDr776aoDCqmWGU1JSaIRnZGSEvGLKJ5rq6+ttNhsdsD179ux//OMfIT/d7UP5F0QMAwBEWH19PRsmTQj56KOP2FujtizpQkl0X5PJVFRUdOPGjTDVc8+ePampqeznwsaNG1UF0A4OHrtWiGEAgAij93dZv/Rnn32mKuAdb3/6058eeeSRlJQUttgw09raOjIyMp76BJgt6/PPP587dy57iFk5PFt1dxmRrIJOaQAAjcrKymIhKgiC93qF7Bv81KlTJSUlxIsyiXft2qXa6xaour6Vr4eGhqqqqoxGI53i45577vnwww9v+US3FZ+XFDEMABBhy5YtYzman5+velf5nFJycjIhxOFwKHOXvtbpdG63e+nSpaGtm78sb21tNRqNdOYvvV6/ZcuW0J53Srp69ar3RsQwAEDksSeCiouLA8yMkZuby6JXkqTU1FSz2UxjeMmSJf72GqsgRz7v3LnT6XRmZ2cLgiBJ0qxZs44fPz7+s09VhYWFhBDvS4QYBgCIvIyMDJqvpaWlHv/J19fXt2jRohUrVmzevNnj8QwNDdntdoPBwHFcc3Ozd/lbTuUgdxwYGMjNzbVaraIoEkL0en1NTc14zjslybK8ZcsW+mtp5cqVqncRwwAAkccGPJeVlQW5C426hIQE2pJes2ZNOCsYSFtbW2pqalRUFK1JZWWlqsDtmcrsUw8NDbF7B1VVVaqrgRgGAIg8NjX0gw8+GPxeAwMDgiDQ/H7qqafCV71R9fT0pKen04em6JqMbLz3bZXBPvvzjx07xlar1Ov1iGEAAM0xGo30a3rVqlXB59aXX37JbhW/8MILYa1hMO6++242cCwxMXH37t2qArdVJFOyLD/66KOsNdzY2OjB9B0AAJoiy7Jer6ff1N5f0/528Xg8//73v1nsrVu3biLqOpo1a9aYzebo6GhCiCiKhYWFnoAPIk9Jqs/LFqNMT08fHh5GaxgAQFuuXLnC0vTuu+/2jJZV7N0vvviC7UhHSkecLMvPPvvsjBkzWMWsVisdHjzlA9j714Ysy5s2baI/sDiO27Nnj/deiGEAgAi7dOkSC63p06cHuZQvLcB2zMvLm4i6jlYf6p133snIyHA4HIIgCIIQFxdXVFTkuQ2SmFL+BZW/k4aGhpQFKMQwAECEffrpp0Qh+B1lWWZDtB577LHw1TB4LGDOnTtXWFio0+kEQaDzbRUUFHz77beRrV64qX5nfPLJJ+zP6m8xDMQwAECEKWOY4zhP0J3SHo+noaHB5XL985//DHstg6as3tq1a1NTU9mcX5Ik0SeebxOVlZX0g7tcrps3b/osgxgGAIg81qj12RoOPpUDvBWpVYE7Ozvj4+P1ej1tExsMhtLS0hMnTnj+f+etxnlXMpjrSWc1IYRs2rQJSzsAAGgXW+vQe5YlSrXWwqgCD06eyOSTZfno0aNpaWl0+DRlMpnefvttn1WK1M+FUQX5c4c5evQo7QZITk6+fPmyv8+FGAYAiLxz587Nnz9///79yo3+GotBjt4KpuTEkGW5v7/f5XIZjUaz2UybxYSQnp6eALt4tFT/4eHh6dOnFxQU9Pf3e4K4wsox0itWrBgeHva3F2IYAEArfD7xMmrJYLZHkDJ7qqqqrFYrvUlMCLFYLIcOHfJXeKIrGlB7eztt2trt9m+++Ub5lnczV5bloaGh4uJiQsjMmTOvX7/ufUC0hgEAtEuZwbfcSau1JKPWrVtntVrNZrMoijSM8/PzL168qOx111RTmDp58iTrUa+vr2fb/f11bt68uW7duqKiovfee8+7JFrDAAAaFfgesM+3NHsz1eOnbq2trTNmzIiPj09ISKDdtrNmzerr6wuwY6QoqzF9+nQaw0lJScHcF/j++++/++67kZGRwE18xDAAwGR18uTJP/zhD8uXL583b15aWtodd9whimJ2drbZbKaBkZ+fX19f77NTNLJ6e3tzcnIEQYiPjyc/rHnw8ssva/knRVNTE72qRqPRZ4HAvRf+whgxDAAwaRw+fHjfvn2tra3333+/3W4nPywY4A/HcRaL5ezZs5GuuG/l5eV2uz0lJcVms9EKr1+/XlVGO0nc3t5OCDGbzUaj8caNG8q3xtqdjk5pAACtoCNvKdWXuCzL27dvnz9/vsvlmjNnjsVi8Re3bOyxt/b29sh8sNHQj9nS0jJr1qyoqCi2xlROTs7p06dVxbSgr68vOjqa47ikpKQQHhYxDAAwcS5cuPDiiy/W1dXNmTOntrY2KSlJEASz2fyjH/1o8eLFd9xxh9VqNRqNoihaLBaDwaAMVNrVzFauJYTYbDaHw1FRUVFXV1dcXFxeXp6TkzNr1iyDwVBSUuJyuZxO54EDByL9of2iEfvBBx+kpaXxPM/axHfeeee7776rhblHlL7//ntJkoxGY3JycghHdCOGAQBCT/XtfOPGjcWLF0uSJIoi60b2fuGzk5njOJZPcXFxsbGxiYmJbrf7wIED586d8z6jdpqPAXhH7Lx580RRtNvtFouFzim2aNEi78ITTHVVaa+D2WxWdkqPs3qIYQCAcKFf0A899JBOp2OxSic49HlPlzZ/9Xo9zaHo6OjY2FibzTZ79uyioqIjR4588cUXAU7EXoyMjHgmQx6ravjzn/+cfl5BECwWS1RU1MKFC5Wd9hFEqxoXF0f/QL29vZ4QXWHEMABAGB07dozNF836k51OZ2pqal5e3uLFixsbG3/5y1+uX7++qanpvffea25u3rVr144dO7q7u2VZvnz58qin0H7cBq+zs9PlchkMBlEUaSe8wWB46aWXIl0vj8fj+fzzzwkhkiTxPK96vGo8EMMAAGHB0jEjI4PjOEmSCgoKmpubVXMpe5dXbRzTY8SjPh6jQaoO6uHh4fr6er1ebzQa9Xo9/eHS3NzsXXiCPffcc7RH2mQyhfCwiGEAgPCSZfns2bO0G9NfAc8PPcnKLar/sn8DjF2aAugnam9vp70IbAS10+mkc1BP2EdWnaiuro72Z7jd7hD+CRDDAAAT59ZWa5hETdtb4/MDHj16NDk5med5QRDo6kxOp/Odd96JUB09breb3hjeuXNnCA+LGAYAAK3w/p1RW1tLB7WZTCZ6i72srExVXtmRED5JSUnE/xRatwwxDAAAmlZRUcHzPMdxoijSu8WSJK1YsYK+G+51IOiRBwYG6MNmycnJoT0+YhgAADQhwBwdr7zyyrx581RPeVVUVExY3X7/+9/Tk8bHx4f2yIhhAADQEO/WLWuPzpw5U6fT0eUR6ePUE3az/OjRo/S8bMx2qCCGAQBAWwKEa15eHh1BnZ6ePpFV+vWvf01bwx9++GFoj4wYBgAADQl8r1eW5fLycr1eX1paqtolfPXZt28ffW4qNzc35MdHDAMAwOTAEnrHjh1tbW3eC1KF6bw//elP9Xq9KIovv/xyyA+OGAYAAK0IclqMsa7vOx6nTp2KiYkhhBQUFITj+IhhAIBwmYCQYAffunXrsmXLTp48OcEVmPKefvppeld4+fLlY7qSQRZGDAMAhJG/CbP27du3YsWKtLS0xsbGcS6mK8tybm4ux3H0eZ6srKy2tjafR5vys3GFhPLiXLp0KSEhgc6m2d7e7hnjpQumMGIYACAsAoRreXk5W3NJFEXljBDBJyWbQKqjo0O1XLEkSfX19aH6ILcz9rjw/fffP2phn/eqR/07IoYBAMLFO1PPnj07c+ZM5TQUBoNBkqSvv/7ae6/APvnkk4ceeqi8vPyBBx7wXrqY47jNmzf7rAyoBLgyVquVPqM8akmfBdAaBgDQkO7ubjoXI6XT6dhr5eM3QbLb7SzO6QuLxVJTUxMVFUU3xsbG7tq1y+e+iGQVn/cONm/eTK9kZmZm+E6NGAYACBdla/jmzZvsLiMhJCoqavHixQsXLqRbfvKTn6h2CWzPnj08z7OlDnp6eg4dOnTt2jWPx3Py5Emn00nPEhMT880333hwV/iWVFdX04vc0dEx1n2Dv86IYQCAMGJfx1lZWSyDBUHYsWOHx+M5duwY7ZfOysoaU0Dm5+ezdvCNGzdUp+vr66PLARFCKisrVTWBYAwODiYmJhJCrFYr3aJa6dnbrV1hxDAAQBjRr+bW1lblzeA33niDvrtmzRq6MS8vzxP09/jVq1dpzzPHcexhVlVIvPHGG4IgmEym6Ojoq1ev+qsYUMrhVCdOnFiyZAldXZFyOp1lZWUdHR0ff/xxkNftwIEDNTU1Cxcu/PTTTwOXRAwDAITdggULCCF07fpnn32WbV+yZAlN08LCQo//p5tUtm/fTveKjY09c+aMv5OWlJTQxnd1dTULaaRvALIs/+Uvf1EGML3OqpWdTCaTy+VasGBBdXX1b3/724MHD+7du/eVV145cuTI1q1bt2zZwroiCCF2uz3wSRHDAAAh5h11jY2N7Hv5+vXrbHtmZib9il+7dq2/43gPvt24cSM9lNvtDnD2jz76iPzwTNQ4P9Hto6qqiv5FVNHLcZzBYCB+KAurXj/++OOBz4gYBgAIC2V8XrhwgX4vOxwOZbjOmDGD4zie5z1jaafSgV2EkKVLlwY49c2bNw0Gg8ViiY2NHRkZ8Vc3UKqrqyOE0EWcDAZDXV1dc3NzbW1tSUlJbm5uXl6eKIr0XWVae2c2+/cXv/hF4DMihgEAQsznsOS2traysrLDhw+z7bt27aLf2uyx1FEPSDmdTrrjunXr/J2U/ssacJ999tn4P9fURq/Y8ePH6RWLiYnp6uryWayvr6+zs3PDhg1PP/308uXLFy1aVFpa2tDQkJeXV1RUVFpa2tTUVFVV9dVXX50/f37U8yKGAQAmGv3GLykpod/4LpdLud3j1R2tjOFz587RRfcEQXjuuec8AUfwOhwOQgjP84jhIMmyHBcXl5GRcenSJZ/veoLrS8ADSwAAERPMVEqDg4Nms5nG8Pbt2/0V89bd3c3zPO3w3LZtW+AKsLFCo47XBSaYWbgD/HesHf6IYQCAMPL3pfyvf/2LBmRSUtKohZXOnDnDcRx9Eun06dMBzkgDmxCi1+tV7+LesDd/w9SDvFa3PEEKYhgAILx8fi8/+uijNIafeOKJYMozH3/8Md1REISenp4AJZubm+lgIjYBBYSK6kbAWJdzUEIMAwCEkc9v5L6+PjYVJe2RDn7fgwcP0lG40dHR+/fv97fjwMCA3W4nhEiStHLlysDHhAhCDAMAhJcy+c6fP/+zn/1MFEV6c9dut7/++utB7ktdvHiRhivHca+++qq/HR977DFaxmKxvPXWW8qjIYk1BTEMABAuqsB76qmnlFMysRd2u33jxo39/f3BzFo8MjJiMBjopBy/+c1vfBY7ffo0PXh0dPQjjzwSyo8EoYYYBgAIO1mWldNK+5uD6YEHHgjmaDk5OTzPm0wmt9vtHdtXrlyhSzkRQuLi4np7ez1oAWsYYhgAIMS8n/odHByMjo5WzbVEp5hmay6xibH27Nnj77D0mJWVlfSZJaPReOHCBVWxsrIyeii9Xr9hwwZVrUBrEMMAAKGnyryVK1eyhq/ZbNbpdG63u7+//9SpU0uXLnU4HMpIJoTU1dUFOPjBgwdZbLe2tirfWrZsGQt1l8v13XffqWqF28NagxgGAAgx70dIc3NzlQ1fSZLYfBq0zKZNm+iMVyyJVUdTPR6TmprK7is3NDT8/e9/b2troxv1ej0hJD4+fvfu3YFrBVqAGAYACK+LFy+yx5MMBoPJZGpublYWYI1UttLtnDlzVAVUx/zVr35FG9B0Ki7VsC+j0fj888/73BG0BjEMABBe3d3dLCBFUbznnnvGn46yLBcVFdlsNkLItGnTaAuY3XJev359SGoOEwAxDAAQFixrt27dyjIyJibm1KlToTpyVlaWKIpsmXpJklwu1+9+9ztVMdAyxDAAQOgpI7C7u5s9xfvkk0+GJB1ZP3ZXV9fatWtramo2btwYeCYQ0CbEMABAiHkH7bx582w2m78xU+M8Plq9kxpiGAAgjPyt2+Pv3fGfJRzHh/BBDAMAhIXPNmtYcxGhOxkhhgEAQi+sTdIgO6WRypMCYhgAYGpCDE8KiGEAAICIQQwDAABEzP8BvvKyH363yYYAAAAASUVORK5CYII=" alt> <strong><em>(A1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"> </span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(R' \cap L) = \frac{{11}}{{20}} \times \frac{3}{{20}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(L) = \frac{9}{{20}} \times \frac{7}{{20}} + \frac{{11}}{{20}} \times \frac{3}{{20}}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(R'|L) = \frac{{{\text{P}}(R' \cap L)}}{{{\text{P}}(L)}}\) <strong><em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{33}}{{96}}{\text{ }}\left( { = \frac{{11}}{{32}}} \right)\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 27.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[5 marks]</em></strong></span></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 28.0px Helvetica;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was generally well answered with candidates who drew a tree diagram being the most successful.</span></p>
</div>
<br><hr><br><div class="specification">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">On a particular day, the probability that it rains is \(\frac{2}{5}\) . The probability that the “Tigers” soccer team wins on a day when it rains is \(\frac{2}{7}\) and the probability that they win on a day when it does not rain is \(\frac{4}{7}\).</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Draw a tree diagram to represent these events and their outcomes.</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">What is the probability that the “Tigers” soccer team wins?</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 style="margin: 0.0px 0.0px 0.0px 0.0px; font: 12.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">Given that the “Tigers” soccer team won, what is the probability that it rained on that day?</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">let R be “it rains” and W be “the ‘Tigers’ soccer team win”</span><img src="data:image/png;base64,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" alt><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em> A1<br></em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[1 mark]</span><br></em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(W) = \frac{2}{5} \times \frac{2}{7} + \frac{3}{5} \times \frac{4}{7}\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{{16}}{{35}}\) <strong> <em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><strong><em><span style="font-family: 'times new roman', times; font-size: medium;">[2 marks]</span><br></em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\({\text{P}}(R\left| W \right.) = \frac{{\frac{2}{5} \times \frac{2}{7}}}{{\frac{{16}}{{35}}}}\) <strong> <em>(M1)</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;">\( = \frac{1}{4}\) <strong><em>A1</em></strong></span></p>
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 11.0px Times;"><span style="font-family: 'times new roman', times; font-size: medium;"><strong><em>[2 marks]</em></strong></span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered in general.</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered in general.</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="margin: 0.0px 0.0px 0.0px 0.0px; font: 10.0px Arial;"><span style="font-family: 'times new roman', times; font-size: medium;">This question was well answered in general.</span></p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p class="p1">A continuous random variable <em>\(T\)</em> has probability density function <em>\(f\)</em> defined by</p>
<p class="p1">\[f(t) = \left\{ {\begin{array}{*{20}{c}} {\left| {2 - t} \right|,}&{1 \le t \le 3} \\ {0,}&{{\text{otherwise.}}} \end{array}} \right.\]</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Sketch the graph of \(y = f(t)\).</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">Find the interquartile range of \(T\).</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1"><img 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" alt></p>
<p>\(\left| {2 - t} \right|\) correct for \(\left[ {1,{\text{ }}2} \right]\) <strong><em>A1</em></strong></p>
<p>\(\left| {2 - t} \right|\) correct for \(\left[ {2,{\text{ }}3} \right]\) <strong><em>A1</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1"><strong>EITHER</strong></p>
<p class="p1">let \({q_1}\) be the lower quartile and let \({q_3}\) be the upper quartile</p>
<p class="p1">let \(d = 2 - {q_1}{\text{ }}( = {q_3} - 2)\) and so \({\text{IQR}} = 2d\) by symmetry</p>
<p class="p1">use of area formulae to obtain \(\frac{1}{2}{d^2} = \frac{1}{4}\)</p>
<p class="p1">(or equivalent) <span class="Apple-converted-space"> </span><span class="s1"><strong><em>M1A1</em></strong></span></p>
<p class="p1">\(d = \frac{1}{{\sqrt 2 }}\) or the value of at least one \(q\). <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>OR</strong></p>
<p class="p1">let \({q_1}\) be the lower quartile</p>
<p class="p1">consider \(\int_1^{{q_1}} {(2 - t){\text{d}}t = \frac{1}{4}} \) <span class="Apple-converted-space"> </span><strong><em>M1A1</em></strong></p>
<p class="p1">obtain \({q_1} = 2 - \frac{1}{{\sqrt 2 }}\) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p1"><strong>THEN</strong></p>
<p class="p1">\({\text{IQR}} = \sqrt 2 \) <span class="Apple-converted-space"> </span><strong><em>A1</em></strong></p>
<p class="p2"> </p>
<p class="p1"><strong>Note: <span class="Apple-converted-space"> </span></strong>Only accept this final answer for the <strong><em>A1</em></strong>.</p>
<p class="p1"><em><strong>[4 marks]</strong></em></p>
<p class="p1"><em><strong>Total [6 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p class="p1">The sketched graphs were mostly acceptable, but sometimes scrappy.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p class="p1">Most candidates had some idea about the upper and lower quartiles, but some were rather vague about how to calculate them for this probability density function. Even those who integrated for the lower quartile often made algebraic mistakes in calculating its value.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br>