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@ -185,7 +185,7 @@ Mean : 43117.75, Median : 44627.5, Mode : 4978
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<h1>
Day 3 - Conditionnal probability
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<time class="published" datetime="2018-11-10T11:24:00+01:00">
10 novembre 2018
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<h2>Conditionnal probability</h2>
<h3>Problem</h3>
<p>Suppose a family has 2 children, one of which is a boy. What is the probability that both children are boys?</p>
<h3>Mathematical explanation</h3>
<p>Let's look at the possible outcomes :
<div>
<style scoped="">
.dataframe tbody tr th:only-of-type {
vertical-align: middle;
}</p>
<div class="highlight"><pre><span></span><span class="na">.dataframe</span> <span class="no">tbody</span> <span class="no">tr</span> <span class="no">th</span> <span class="err">{</span>
<span class="nl">vertical-align:</span> <span class="nf">top</span><span class="c">;</span>
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</pre></div>
<p></style>
<table class="dataframe" border="1">
<thead>
<tr style="text-align: right;">
<th></th>
<th>B</th>
<th>G</th>
</tr>
</thead>
<tbody>
<tr>
<th>B</th>
<td>BB</td>
<td>BG</td>
</tr>
<tr>
<th>G</th>
<td>GB</td>
<td>GG</td>
</tr>
</tbody>
</table>
</div></p>
<p>We know that at least one of the children is a boy, so only "GG" is not possible. The event where the family has a new boy is then "BB". Hence the probability is :
</p>
<div class="math">$$\frac{BB}{BB+GB+BG}=\frac{1}{3}$$</div>
<h2>Draw 2 cards from a deck</h2>
<h3>Problem</h3>
<p>You 2 draw cards from a standard 52-card deck without replacing them. What is the probability that both cards are of the same suit?</p>
<h3>Mathematical explanation</h3>
<p>There are 13 cards of each suit. Draw one card. It can be anything with probability of 1. Now there are 51 cards left and 12 of them are the same suit as the first card you drew. So the chance the second card matches the 1st is <span class="math">\(\frac{12}{51}\)</span>.</p>
<h2>Drawing marbles</h2>
<h3>Problem</h3>
<p>A bag contains 3 red marbles and 4 blue marbles. Then, 2 marbles are drawn from the bag, at random, without replacement. If the first marble drawn is red, what is the probability that the second marble is blue?</p>
<h3>Mathematical explanation</h3>
<p>On the first draw, the probabilities are the following :
we call B the event "a blue ball is drawn" and R the event "a red ball is drawn"
<em> <span class="math">\(P(B)=\frac{4}{7}\)</span>
</em> <span class="math">\(P(R)=\frac{3}{7}\)</span></p>
<p>On the second draw, if a red ball has been drawn at first, the probabilities are :
<em> <span class="math">\(P(B|R)=\frac{4}{6}\)</span>
</em> <span class="math">\(P(R|R)=\frac{2}{6}\)</span></p>
<p>Hence, the probability of drawing a blue ball if the first ball drawn was red is <span class="math">\(\frac{1}{3}\)</span></p>
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<li><a href="./blog/Statistics_10days-day3.html">11/18 Day 3 - Conditionnal probability</a></li>
<li><a href="./blog/Statistics_10days-day2.html">11/18 Day 2 - Probability, Compound Event Probability</a></li>
<li><a href="./blog/Statistics_10days-day1.html">11/18 Day 1 - Quartiles, Interquartile Range and standard deviation</a></li>
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python/sorting.html
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tipuesearch_content.json
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