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<h2 class="hd hd-2 unit-title">Introduction</h2>
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<p>Read <a href="/assets/courseware/v1/55388d0255570f719bcb5809a37bc35d/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_Session28.pdf" target="[object Object]">Chapter 16.1–16.5 (PDF)</a> of <em>Mathematics for Computer Science</em> for 4.1 Intro to Discrete Probability.</p>
<p>View the <a href="/assets/courseware/v1/8717a06ffd5ecd5bba2c3379156a8956/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_cp28.pdf" target="[object Object]">Section 4.1 In-Class Questions (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Tree Model</h2>
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<h3 class="hd hd-2">Tree Model</h3>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/581c6ea750d65f6c79d68ba06896d5c7/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_tree_model.pdf" target="[object Object]">Tree Model (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Exercise | Socks and Shoes</h2>
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Socks and Shoes
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p> Parker has two pairs of black shoes and three pairs of brown shoes. He also has three pairs of red socks, four pairs of brown socks and six pairs of black socks.</p>
<p>Now let's say that Parker chooses a pair of shoes at random and a pair of socks at random. We would like to know the probability of him choosing shoes and socks of the same color.</p>
<br/>
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<option value="a pair of shoes"> a pair of shoes</option>
<option value="a pair of socks"> a pair of socks</option>
<option value="a pair of colors"> a pair of colors</option>
<option value="all permutations of shoes and socks"> all permutations of shoes and socks</option>
<option value="a color"> a color</option>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><p> 2.<strong> Identify the event of interest! </strong></p>
<p> a. How many outcomes are there in total? </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 4" role="group"><p> 3.<strong> Assign outcome probabilities </strong></p>
<p><em> Please answer in the form of decimals with four significant digits.</em> </p>
<p> a. What is the probability of choosing black shoes? </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 5" role="group"><p> b. What is the probability of choosing red socks? </p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 6" role="group"><p> 4.<strong> Compute event probabilities! </strong></p>
<p><em> Please answer in the form of decimals with four significant digits.</em> </p>
<p> What is the probability that he chooses shoes and socks of the same color? </p>
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<h2 class="hd hd-2 unit-title">Lecture Video | Simplified Monty Hall Tree</h2>
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<h3 class="hd hd-2">Simplified Monty Hall Tree</h3>
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<p>Download a copy of the slides for <a href="/assets/courseware/v1/791e6dcd25b949ba8e497ce775b3156e/asset-v1:OCW+6.042J+2T2019+type@asset+block/MIT6_042JS15_SmplifiedMonty.pdf" target="[object Object]">Simplified Monty Hall Tree (PDF)</a></p>
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<h2 class="hd hd-2 unit-title">Exercise | Simplify Prize Tree</h2>
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Simplify Prize Tree
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<input type="checkbox" name="input_a6e92e112d144e8b8379dd255403840c_2_1[]" id="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_1" class="field-input input-checkbox" value="choice_1"/><label id="a6e92e112d144e8b8379dd255403840c_2_1-choice_1-label" for="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_a6e92e112d144e8b8379dd255403840c_2_1"> Branches after the prize location nodes are symmetric.
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<input type="checkbox" name="input_a6e92e112d144e8b8379dd255403840c_2_1[]" id="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_3" class="field-input input-checkbox" value="choice_3"/><label id="a6e92e112d144e8b8379dd255403840c_2_1-choice_3-label" for="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_3" class="response-label field-label label-inline" aria-describedby="status_a6e92e112d144e8b8379dd255403840c_2_1"> The door that conceals the prize and the door that the contestant picks can be condensed into whether the contestant picks the door with the prize.
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<input type="checkbox" name="input_a6e92e112d144e8b8379dd255403840c_2_1[]" id="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_4" class="field-input input-checkbox" value="choice_4"/><label id="a6e92e112d144e8b8379dd255403840c_2_1-choice_4-label" for="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_4" class="response-label field-label label-inline" aria-describedby="status_a6e92e112d144e8b8379dd255403840c_2_1"> If the door that conceals the prize is picked initially, the SWITCH strategy leads to losing, independent of which door is opened.
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<input type="checkbox" name="input_a6e92e112d144e8b8379dd255403840c_2_1[]" id="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_5" class="field-input input-checkbox" value="choice_5"/><label id="a6e92e112d144e8b8379dd255403840c_2_1-choice_5-label" for="input_a6e92e112d144e8b8379dd255403840c_2_1_choice_5" class="response-label field-label label-inline" aria-describedby="status_a6e92e112d144e8b8379dd255403840c_2_1"> The branches that follow the two nodes where a door concealing a goat is picked, lead to the same outcome with the same probability, so these nodes could be combined.
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<h2 class="hd hd-2 unit-title">Exercise | Sum Rule Practice</h2>
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Sum Rule Practice
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<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
<mo>,</mo>
<msub>
<mi>E</mi>
<mn>1</mn>
</msub>
<mo>,</mo>
</math> and <math xmlns="http://www.w3.org/1998/Math/MathML">
<msub>
<mi>E</mi>
<mn>2</mn>
</msub>
</math>. The probability of each one occurring is <math xmlns="http://www.w3.org/1998/Math/MathML">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math> . What is the probability that any one of these events occurs?
<br/>
<br/>
<em>Enter answers as a decimal.</em></label>
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<h2 class="hd hd-2 unit-title">Exercise | Additional Rule</h2>
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Addition Rule
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p> What is the probability that you roll a total of 7 or 11 when you roll two dice?
<br/>
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<em>Enter your answer as a decimal with two significant figures.</em></p>
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<h2 class="hd hd-2 unit-title">Exercise | Fun With Coins</h2>
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Fun With Coins
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p> Answer these following questions about flipping a fair coin. </p>
<p>1. What is the probability that you will throw Tails <em>forever</em> with a fair coin?</p>
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<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><p>2. What is the probability that you will throw at least one Head when you keep throwing a fair coin <em>forever?</em></p>
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<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="False">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>