# 08_25_2ans - STAT 400 1 Fall 2011 Examples for(2 In...

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STAT 400 Examples for 08/25/2011 (2) Fall 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. P( M ) = 0.60, P( U | M ) = 0.06, P( U | F ) = 0.045. a) What is the probability that the person selected is a male and is unemployed? P( M U ) = P( M ) × P( U | M ) = 0.60 × 0.06 = 0.036 . b) What is the probability that the person selected is a female and is unemployed? P( F U ) = P( F ) × P( U | F ) = 0.40 × 0.045 = 0.018 . Unemployed Employed Total Male 0.036 0.564 0.60 Female 0.018 0.382 0.40 Total . 0.054 0.946 1.00 c) What is the probability that the person selected is unemployed? P( U ) = 0.036 + 0.018 = 0.054 . OR Law of Total Probability: P( U ) = P( M ) × P( U | M ) + P( F ) × P( U | F ) = 0.60 × 0.06 + 0.40 × 0.045 = 0.054 . d)

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## This note was uploaded on 11/07/2011 for the course STAT 400 taught by Professor Kim during the Fall '08 term at University of Illinois, Urbana Champaign.

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08_25_2ans - STAT 400 1 Fall 2011 Examples for(2 In...

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