47 lines
2.5 KiB
HTML
Executable File
47 lines
2.5 KiB
HTML
Executable File
<!DOCTYPE html>
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<html lang="en-US" dir="ltr">
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<!--******************************************-->
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<!--* Authored with PreTeXt *-->
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<!--* pretextbook.org *-->
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<!--* Theme: boulder *-->
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<!--* Palette: *-->
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<!--******************************************-->
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<!--********************************************-->
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<!--* Generated from PreTeXt source *-->
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<!--* *-->
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<!--* https://pretextbook.org *-->
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<!--* *-->
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<!--********************************************-->
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
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<meta name="robots" content="noindex, nofollow">
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</head>
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<body class="ignore-math">
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<article class="example example-like"><h5 class="heading">
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">25</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h5>
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<div class="para logical">
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<div class="para">Continuing from the previous example, <span class="process-math">\(|\Omega| = 36\text{.}\)</span>
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</div>
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<div class="displaymath process-math">
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\begin{align*}
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A \amp = \{(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)\} \\
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B \amp = \{(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\} \\
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A \cap B \amp = \{(6, 4), (6, 5), (6, 6)\}
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\end{align*}
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</div>
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<div class="para">So <span class="process-math">\(\Pr(A) = \frac{6}{36}, \Pr(B) = \frac{6}{36}, \text{and } \Pr(A\cap B) = \frac{3}{36}\text{.}\)</span> Then:</div>
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<div class="displaymath process-math">
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\begin{gather*}
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\Pr(A \mid B) = \frac{\Pr(A\cap B)}{\Pr(B)} = \frac{3/36}{6/36} = \frac{3}{6} = \frac{1}{2}.
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\end{gather*}
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</div>
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<div class="para">Notice that <span class="process-math">\(\Pr(A\mid B)\)</span> is significantly larger than <span class="process-math">\(\Pr(A)\text{.}\)</span>
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</div>
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<div class="autopermalink" data-description="Paragraph"><a href="#example-rolls-conditional-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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</div>
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<div class="autopermalink" data-description="Example 25"><a href="#example-rolls-conditional" title="Copy heading and permalink for Example 25" aria-label="Copy heading and permalink for Example 25">🔗</a></div></article><span class="incontext"><a class="internal" href="notes-week-01.html#example-rolls-conditional">in-context</a></span>
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</body>
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</html>
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