{"id":97,"date":"2020-02-07T15:50:56","date_gmt":"2020-02-07T20:50:56","guid":{"rendered":"https:\/\/pressbooks.library.torontomu.ca\/pohmath\/chapter\/7-5-practice-question-answers\/"},"modified":"2023-11-27T14:19:26","modified_gmt":"2023-11-27T19:19:26","slug":"7-5-practice-question-answers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.library.torontomu.ca\/pohmath\/chapter\/7-5-practice-question-answers\/","title":{"raw":"7.5. Practice question answers","rendered":"7.5. Practice question answers"},"content":{"raw":"[Latexpage]\n

Chapter 7 practice question answers<\/h1>\n
\n

7.1. Binomial Probability<\/strong><\/p>\n\n<\/header>\n

\n\n1.<\/strong>\u00a0 \u2248 0.0322\n\n2.<\/strong>\u00a0 a.\u00a0<\/strong>0.0064\n\n\u00a0 \u00a0 \u00a0b. <\/strong>0.2048\n\n\u00a0 \u00a0 \u00a0c.<\/strong> 0.9421\n\n3.<\/strong>\u00a0 a. \u2248\u00a0<\/strong>0.1047\n\n\u00a0 \u00a0 \u00a0b. \u2248\u00a0<\/strong>0.0604\n\n\u00a0 \u00a0 \u00a0c.<\/strong> \u2248 0.0269\n\n\u00a0 \u00a0 \u00a0d.<\/strong> \u2248 0.2026\n\n4.<\/strong>\u00a0a. \u2248\u00a0<\/strong>0.3650\n\n\u00a0 \u00a0 b. \u2248 <\/strong>0.2305\n\n5. \u2248\u00a0<\/strong>0.6778\n\n<\/div>\n<\/div>\n
\n

7.2. Bayes' Formula<\/strong><\/p>\n\n<\/header>\n

\n\n1.\u00a0 a. <\/strong>31\/48\n\n\u00a0 \u00a0 \u00a0b.<\/strong> 8\/17\n\n\u00a0 \u00a0 \u00a0c.<\/strong> 5\/8\n\n2.\u00a0 a. <\/strong>0.125\n\n\u00a0 \u00a0 \u00a0b.<\/strong> \u2248\u00a0<\/strong>0.7241\n\n3.\u00a0 a. <\/strong>0.045\n\n\u00a0 \u00a0 \u00a0b.<\/strong> \u2248 0.2667\n\n\u00a0 \u00a0 \u00a0c.<\/strong> 0.03\n\n4.\u00a0 a. <\/strong>0.0572\n\n\u00a0 \u00a0 \u00a0b.<\/strong> 0.07\n\n\u00a0 \u00a0 \u00a0c.<\/strong> \u2248 0.0446\n\n<\/div>\n<\/div>\n \n
\n

7.3. Expected Value and Tree Diagrams<\/strong><\/p>\n\n<\/header>\n

\n\n1.\u00a0<\/strong> 1.7\n\n2.\u00a0<\/strong> \u2248 -0.83 cents\n\n3.\u00a0<\/strong> -0.96 cents\n\n4.\u00a0<\/strong> \u2248 -0.0519 cents\n\n5.\u00a0<\/strong> 0.94\n\n6.\u00a0 \u2248\u00a0<\/strong>0.5177\n\n7.\u00a0\u00a0<\/strong>0.776\n\n8.\u00a0<\/strong> 0.97\n\n<\/div>\n<\/div>\n \n
\n

7.4. Markov Chains<\/strong><\/p>\n\n<\/header>\n

\n\n1.\u00a0<\/strong>\n
\\begin{equation*}\n\\mathbf{First\\; Purchase\\quad\\quad}\n\\begin{blockarray}{*{3}{c} l}\n\\begin{block}{*{3}{>{$\\footnotesize}c<{$}} l} & \\BAmulticolumn{3}{c}{\\textbf{Next Purchase}} & \\\\ & \\quad Ford\\quad\\quad & \\quad GM\\quad\\quad \\\\ \\end{block} \\begin{block}{>{$\\footnotesize}l<{$}[*{3}{c}]}\nFord & 0.60 & 0.40 \\\\\nGM & 0.20 & 0.80 \\\\\n\\end{block}\n\\end{blockarray}\n\\end{equation*}<\/div>\n2.\u00a0 <\/strong>a.\u00a0<\/strong> 0.32\n\n\u00a0 \u00a0 \u00a0b.<\/strong>\u00a0 Shoot (S) = $2\/3$, Pass (P) = $1\/3$\n\n3.\u00a0 a.\u00a0<\/strong> 31%\n\n\u00a0 \u00a0 \u00a0b.<\/strong>\u00a0 25%\n\n4<\/strong>. a.\u00a0<\/strong>\n
\\begin{equation*}\n\\mathbf{Before\\quad\\quad}\n\\begin{blockarray}{*{3}{c} l}\n\\begin{block}{*{3}{>{$\\footnotesize}c<{$}} l} & \\BAmulticolumn{3}{c}{\\textbf{After}} & \\\\ & \\quad Y\\quad\\quad & \\quad N\\quad\\quad \\\\ \\end{block} \\begin{block}{>{$\\footnotesize}l<{$}[*{3}{c}]}\nReported accident (Y) & 0.25 & 0.75 \\\\\nDidn't report accident (N) & 0.05 & 0.95 \\\\\n\\end{block}\n\\end{blockarray}\n\\end{equation*}<\/div>\n
\n\n\u00a0 \u00a0 \u00a0b.\u00a0<\/strong> 680\n\n\u00a0 \u00a0 \u00a0c.<\/strong>\u00a0 561\n\n\u00a0 \u00a0 \u00a0d.<\/strong>\u00a0 6.25%\n\n<\/div>\n<\/div>\n<\/div>\n ","rendered":"

Chapter 7 practice question answers<\/h1>\n
\n
\n

7.1. Binomial Probability<\/strong><\/p>\n<\/header>\n

\n

1.<\/strong>\u00a0 \u2248 0.0322<\/p>\n

2.<\/strong>\u00a0 a.\u00a0<\/strong>0.0064<\/p>\n

\u00a0 \u00a0 \u00a0b. <\/strong>0.2048<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong> 0.9421<\/p>\n

3.<\/strong>\u00a0 a. \u2248\u00a0<\/strong>0.1047<\/p>\n

\u00a0 \u00a0 \u00a0b. \u2248\u00a0<\/strong>0.0604<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong> \u2248 0.0269<\/p>\n

\u00a0 \u00a0 \u00a0d.<\/strong> \u2248 0.2026<\/p>\n

4.<\/strong>\u00a0a. \u2248\u00a0<\/strong>0.3650<\/p>\n

\u00a0 \u00a0 b. \u2248 <\/strong>0.2305<\/p>\n

5. \u2248\u00a0<\/strong>0.6778<\/p>\n<\/div>\n<\/div>\n

\n
\n

7.2. Bayes’ Formula<\/strong><\/p>\n<\/header>\n

\n

1.\u00a0 a. <\/strong>31\/48<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong> 8\/17<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong> 5\/8<\/p>\n

2.\u00a0 a. <\/strong>0.125<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong> \u2248\u00a0<\/strong>0.7241<\/p>\n

3.\u00a0 a. <\/strong>0.045<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong> \u2248 0.2667<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong> 0.03<\/p>\n

4.\u00a0 a. <\/strong>0.0572<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong> 0.07<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong> \u2248 0.0446<\/p>\n<\/div>\n<\/div>\n

 <\/p>\n

\n
\n

7.3. Expected Value and Tree Diagrams<\/strong><\/p>\n<\/header>\n

\n

1.\u00a0<\/strong> 1.7<\/p>\n

2.\u00a0<\/strong> \u2248 -0.83 cents<\/p>\n

3.\u00a0<\/strong> -0.96 cents<\/p>\n

4.\u00a0<\/strong> \u2248 -0.0519 cents<\/p>\n

5.\u00a0<\/strong> 0.94<\/p>\n

6.\u00a0 \u2248\u00a0<\/strong>0.5177<\/p>\n

7.\u00a0\u00a0<\/strong>0.776<\/p>\n

8.\u00a0<\/strong> 0.97<\/p>\n<\/div>\n<\/div>\n

 <\/p>\n

\n
\n

7.4. Markov Chains<\/strong><\/p>\n<\/header>\n

\n

1.\u00a0<\/strong><\/p>\n

\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n<\/div>\n

2.\u00a0 <\/strong>a.\u00a0<\/strong> 0.32<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong>\u00a0 Shoot (S) = \"2/3\", Pass (P) = \"1/3\"<\/p>\n

3.\u00a0 a.\u00a0<\/strong> 31%<\/p>\n

\u00a0 \u00a0 \u00a0b.<\/strong>\u00a0 25%<\/p>\n

4<\/strong>. a.\u00a0<\/strong><\/p>\n

\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n<\/div>\n

\n

\u00a0 \u00a0 \u00a0b.\u00a0<\/strong> 680<\/p>\n

\u00a0 \u00a0 \u00a0c.<\/strong>\u00a0 561<\/p>\n

\u00a0 \u00a0 \u00a0d.<\/strong>\u00a0 6.25%<\/p>\n<\/div>\n<\/div>\n<\/div>\n

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