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<h2 class="hd hd-2 unit-title">Introduction</h2>
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<p>Read <a href="/assets/courseware/v1/719e1038eca434492b93878d25b122db/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_Session29.pdf" target="[object Object]">Chapter 17.1–17.5 (PDF)</a> of <em>Mathematics for Computer Science</em> for 4.2 Conditional Probability.</p>
<p>View the <a href="/assets/courseware/v1/e27b72c14eb731f7c9d9acb9b3ba61cc/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_cp29.pdf" target="[object Object]">Section 4.2 In-Class Questions (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Conditional Probability Definitions</h2>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/b8af1717452c829723312bce607aba1e/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_ConditProbability.pdf" target="[object Object]">Conditional Probability (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Exercise | Dicey Sum</h2>
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Dicey Sum
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<h2 class="hd hd-2 unit-title">Lecture Video | Law of Total Probability</h2>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/9c6b40b913efc9db73e075282e001b98/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_LawTotalProbab.pdf" target="[object Object]">Law of Total Probability (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Exercise | Cavities and Candy</h2>
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Cavities And Candy
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<label class="problem-group-label" for="input_19817b3eb0484111bbe4b70c0223ee10_2_1" id="label_19817b3eb0484111bbe4b70c0223ee10_2_1">Say the probability I have a cavity is <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math> and the probability I do not have a cavity is <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>3</mn>
<mn>4</mn>
</mfrac>
</math>. If I have a cavity, then I eat candy with probability <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
</math>. If I do not have a cavity, then I eat candy with probability <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>1</mn>
<mn>3</mn>
</mfrac>
</math>.
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<br/>
What is the probability that I will eat candy?
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<em> Please answer in the form of a decimal with two significant digits.</em></label>
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<h2 class="hd hd-2 unit-title">Lecture Video | Bayes' Theorem</h2>
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<h2 class="hd hd-2 unit-title">Exercise | Two Boys</h2>
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Two Boys
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>A couple has two children, one of which is a boy. What is the probability that they have two boys? .</p>
<p>Assume the probability of having a boy is 50%.</p>
<em> Please answer in the form of a decimal with two significant digits.</em>
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<h2 class="hd hd-2 unit-title">Exercise | Conditional Probability</h2>
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<p>Let </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mi>A</mi> <mo>:=</mo> <mtext>the event that Albert is giving the lecture</mtext> </math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mi>L</mi> <mo>:=</mo> <mtext>the event that Louis Reasoner goes to lecture</mtext> </math></p>
<p>where </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mn>0.8</mn> </math></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mo movablelimits="true" form="prefix">Pr</mo> <mo stretchy="false">[</mo> <mi>L</mi> <mo stretchy="false">]</mo> <mo>=</mo> <mn>0.4</mn> </math></p>
<p>Also, the probability that Louis goes to lecture, given that Albert is giving the lecture, is 0.3.</p>
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<h2 class="hd hd-2 unit-title">Exercise | Dicey Game</h2>
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What is the probability that he wins, given that he obtained a pair the first time?
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Watch Out for Crocodiles
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_6d1d5e1010b4494db76e20d94b278690_2_1" class=" capa_inputtype textline">
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<label class="problem-group-label" for="input_6d1d5e1010b4494db76e20d94b278690_2_1" id="label_6d1d5e1010b4494db76e20d94b278690_2_1">This weekend it will rain with probability <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math>, be sunny with probability <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math>, and hail baseballs otherwise. If it rains, then there is a 50% chance that I will see a crocodile. If it is sunny, then crocodiles will hide themselves from me with probability <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>3</mn>
<mn>8</mn>
</mfrac>
</math>. If it hails, then I will see a crocodile with complete certainty.
<br/>
<br/>
What is the probability I see a crocodile this weekend?
<br/>
<br/>
<em> Please answer as a fraction of the form x/y.</em></label>
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