A recent study shows that unemployment does not impact males and females in the same way (Newsweek, April 20, 2009). According to a Bureau of Labor Statistics report, 8.5% of those who are eligible to work are unemployed. The unemployment rate is 8.8% for eligible men and only 7.0% for eligible women. Suppose 52% of the eligible workforce in the U. S. consists of men.

a. You have just heard that another worker in a large firm has been laid off. What is the probability that this worker is a man?

b. You have just heard that another worker in a large firm has been laid off. What is the probability that this worker is a woman?

A) 0.538 or 53.8%

B) 0.395 or 39.5%

Explanation:

U = unemployed person

M = unemployed is a man

W = unemployed is a woman

we are given the following information:

probability of unemployment = P (U) = 0.085 probability of a man being unemployed = P (UM) = 0.088 probability of a woman being unemployed = P (UW) = 0.07 men in the workforce = P (M) = 0.52 women in the workforce = P (W) = 1 - P (M) = 1 - 0.52 = 0.48

A) the probability that the recently unemployed is a man:

= [P (UM) x P (M) ] / P (U) = (0.088 x 0.52) / 0.085 = 0.538 or 53.8%

B) the probability that the recently unemployed is a woman:

= [P (UW) x P (W) ] / P (U) = (0.07 x 0.48) / 0.085 = 0.395 or 39.5%