53 lines
3.8 KiB
HTML
53 lines
3.8 KiB
HTML
<!DOCTYPE html>
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<html lang="en-US" dir="ltr">
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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"><h2 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">1.1.2</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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</h2>
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<div class="para">An experiment consists of rolling a standard 6-sided die. The sample space is <span class="process-math">\(\Omega = \{1, 2, 3, 4, 5, 6\}\text{.}\)</span> One possible event is <span class="process-math">\(A = \{2, 4, 6\}\text{,}\)</span> i.e., the event that the result of the roll is even.<div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-sample-space-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="para">What would the sample space look like if we roll the die two times and recorded the results?<div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-sample-space-1-2" 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="solutions">
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<details class="answer solution-like born-hidden-knowl"><summary class="knowl__link"><span class="type">Answer</span><span class="period heading-divison-mark heading-divison-mark__period">.</span></summary>
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<div class="answer solution-like knowl__content">
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<div class="para logical">
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<div class="displaymath process-math">
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\begin{align*}
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\Omega = \{\amp (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), \\
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\amp (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), \\
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\amp (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), \\
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\amp (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), \\
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\amp (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), \\
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\amp (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)\}
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\end{align*}
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</div>
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<div class="para">Note that, for example, <span class="process-math">\((1, 2)\)</span> is a different outcome from <span class="process-math">\((2, 1)\text{.}\)</span>
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</div>
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<div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-sample-space-2-1" 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" aria-hidden="true" data-description="Answer 1.1.2.1"><a tabindex="-1" href="#example-sample-space-2" title="Copy heading and permalink for Answer 1.1.2.1" aria-label="Copy heading and permalink for Answer 1.1.2.1">🔗</a></div>
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</div></details>
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</div>
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<div class="autopermalink" aria-hidden="true" data-description="Example 1.1.2"><a tabindex="-1" href="#example-sample-space" title="Copy heading and permalink for Example 1.1.2" aria-label="Copy heading and permalink for Example 1.1.2">🔗</a></div>
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</article><span class="incontext"><a class="internal" href="sec-Set-Theory.html#example-sample-space">In Context</a></span>
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</body>
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</html>
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