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<h2 class="hd hd-2 unit-title">Conditional probability, independendce, Bayes</h2>
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<h2 class="hd hd-2 unit-title">Class 3 reading questions: </h2>
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Problem 1
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<p>
For numeric answers the system can do arithmetic: you can enter your answer as an expression like 17/43 or 16*5/34^2. You can also enter a decimal answer. Give all decimals to 3 places. </p>
<p>
You roll two dice. Consider the following events.<br/>[mathjaxinline]A[/mathjaxinline] = 'first die is 3'<br/>[mathjaxinline]B[/mathjaxinline] = 'sum is 7'<br/>[mathjaxinline]C[/mathjaxinline] = 'sum is greater than or equal to 7' </p>
<p><b class="bf">(a)</b> Compute [mathjaxinline]P(B)[/mathjaxinline].<br/><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_c3-rq11_2_1" class=" capa_inputtype textline">
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<p id="answer_c3-rq11_2_1" class="answer"/>
</div>
</div></div> </p>
<p><b class="bf">(b)</b> Compute [mathjaxinline]P(B|A)[/mathjaxinline].<br/><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_c3-rq11_3_1" class=" capa_inputtype textline">
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<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_c3-rq11_3_1" class="answer"/>
</div>
</div></div> </p>
<p><b class="bf">(c)</b> Compute [mathjaxinline]P(B|C)[/mathjaxinline].<br/><div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_c3-rq11_4_1" class=" capa_inputtype textline">
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<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_c3-rq11_4_1" class="answer"/>
</div>
</div></div> </p>
<p><b class="bf">(d)</b> Are [mathjaxinline]A[/mathjaxinline] and [mathjaxinline]B[/mathjaxinline] independent? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c3-rq11_5_1">
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</label>
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<div class="field">
<input type="radio" name="input_c3-rq11_5_1" id="input_c3-rq11_5_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="c3-rq11_5_1-choice_2-label" for="input_c3-rq11_5_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_c3-rq11_5_1"> <text> No</text>
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<p><b class="bf">(e)</b> Are [mathjaxinline]B[/mathjaxinline] and [mathjaxinline]C[/mathjaxinline] independent? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><div class="choicegroup capa_inputtype" id="inputtype_c3-rq11_6_1">
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Draw two cards from a deck.<br/>Let [mathjaxinline]S_1[/mathjaxinline] = &#8216;first card is a spade'.<br/>Let [mathjaxinline]S_2[/mathjaxinline] = &#8216;second card is a spade'.<br/>What is [mathjaxinline]P(S_2|S_1^ c)[/mathjaxinline]? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_c3-rq12_2_1" class=" capa_inputtype textline">
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Problem 3
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<p>
Start with an urn with 5 red and 3 blue balls in it. Draw one ball. Put that ball back in the urn along with another ball of the same color. Now draw another ball from the urn. </p>
<p><b class="bf">(a)</b> What is the probability the second ball drawn is red? <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_c3-rq13_2_1" class=" capa_inputtype textline">
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<p id="answer_c3-rq13_2_1" class="answer"/>
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</div></div> </p>
<p><b class="bf">(b)</b> Suppose the second ball drawn is red. What is the probability the first ball was blue. <div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_c3-rq13_3_1" class=" capa_inputtype textline">
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Problem 4
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On a scale of 1 to 100 how important is Bayes' Formula for statistics. </p>
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