01_26 - STAT 400 Examples for Spring 2011 1 In Neverland...

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STAT 400 Examples for 01/26/2011 Spring 2011 1. In Neverland, men constitute 60% of the labor force. The rates of unemployment are 6.0% and 4.5% among males and females, respectively. A person is selected at random from Neverland’s labor force. a) What is the probability that the person selected is a male and is unemployed? b) What is the probability that the person selected is a female and is unemployed? Unemployed Employed Total Male Female Total .

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c) What is the probability that the person selected is unemployed? Law of Total Probability : P ( A ) = P ( A B ) + P ( A B ' ) = P ( B ) P ( A B ) + P ( B ' ) P ( A B ' ) In general, P ( A ) = = m i 1 P ( B i ) P ( A B i ) d) Suppose the person selected is unemployed . What is the probability that a male was selected? Bayes' Theorem : P ( B ) P ( A B ) P ( B A ) =                                     , P ( B ) P ( A B ) + P ( B ' ) P ( A B ' ) In general, P ( B k )
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