Question

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?

Answer 1

Answer:

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%