document.write( "Question 1197314: b. A manufacturer of a firm claims that 70% of its new hires turn out to be good workers and the\r
\n" ); document.write( "\n" ); document.write( "rest are to be poor workers. The company advised their current workers to qualify a reasoning\r
\n" ); document.write( "\n" ); document.write( "test. Eighty percent of the good workers and forty percent of the poor workers pass the reasoning test. If the company makes the reasoning test be a part of its hiring procedure, what then is the\r
\n" ); document.write( "\n" ); document.write( "probability of the new hires that,\r
\n" ); document.write( "\n" ); document.write( "i.will turn out to be good workers? (Marks -4]
\n" ); document.write( "ii. will turn out to be poor workers? (Marks-4]\r
\n" ); document.write( "\n" ); document.write( "iii. Depict the turn out percentage of the workers on the Bayes' tree diagram. [Mark-1] \n" ); document.write( "
Algebra.Com's Answer #848361 by onyulee(41)\"\" \"About 
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**i. Probability of a new hire being a good worker given they pass the test:**\r
\n" ); document.write( "\n" ); document.write( "* **Let:**
\n" ); document.write( " * G: Event that a new hire is a good worker
\n" ); document.write( " * P: Event that a new hire passes the reasoning test \r
\n" ); document.write( "\n" ); document.write( "* **Given:**
\n" ); document.write( " * P(G) = 0.70 (Probability of a good worker)
\n" ); document.write( " * P(P|G) = 0.80 (Probability of passing the test given they are a good worker)
\n" ); document.write( " * P(P|G') = 0.40 (Probability of passing the test given they are a poor worker)
\n" ); document.write( " * P(G') = 1 - P(G) = 0.30 (Probability of a poor worker)\r
\n" ); document.write( "\n" ); document.write( "* **Use Bayes' Theorem:**\r
\n" ); document.write( "\n" ); document.write( " P(G|P) = [P(P|G) * P(G)] / [P(P|G) * P(G) + P(P|G') * P(G')]\r
\n" ); document.write( "\n" ); document.write( " P(G|P) = [0.80 * 0.70] / [(0.80 * 0.70) + (0.40 * 0.30)]
\n" ); document.write( " P(G|P) = 0.56 / (0.56 + 0.12)
\n" ); document.write( " P(G|P) = 0.56 / 0.68
\n" ); document.write( " P(G|P) ≈ 0.8235 \r
\n" ); document.write( "\n" ); document.write( "**Therefore, the probability of a new hire being a good worker given they pass the reasoning test is approximately 0.8235 or 82.35%.**\r
\n" ); document.write( "\n" ); document.write( "**ii. Probability of a new hire being a poor worker given they pass the test:**\r
\n" ); document.write( "\n" ); document.write( "* **Use the complement rule:**
\n" ); document.write( " * P(G'|P) = 1 - P(G|P)
\n" ); document.write( " * P(G'|P) = 1 - 0.8235
\n" ); document.write( " * P(G'|P) = 0.1765\r
\n" ); document.write( "\n" ); document.write( "**Therefore, the probability of a new hire being a poor worker given they pass the reasoning test is approximately 0.1765 or 17.65%.**\r
\n" ); document.write( "\n" ); document.write( "**iii. Bayes' Tree Diagram**\r
\n" ); document.write( "\n" ); document.write( "* **Root Node:** \"New Hire\"
\n" ); document.write( "* **Branch 1:** \"Good Worker\" (0.70)
\n" ); document.write( " * Sub-branch: \"Passes Test\" (0.80)
\n" ); document.write( " * Sub-branch: \"Fails Test\" (0.20)
\n" ); document.write( "* **Branch 2:** \"Poor Worker\" (0.30)
\n" ); document.write( " * Sub-branch: \"Passes Test\" (0.40)
\n" ); document.write( " * Sub-branch: \"Fails Test\" (0.60)\r
\n" ); document.write( "\n" ); document.write( "**Note:** The probabilities on the branches of the tree diagram represent the conditional probabilities given the preceding event.\r
\n" ); document.write( "\n" ); document.write( "This analysis shows that implementing the reasoning test significantly increases the likelihood of hiring good workers.
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