Question

"Since the fall of 2008, millions of Americans have lost jobs due to the economic meltdown. A recent study shows that unemployment has not impacted males and females in the same way (Newsweek,April 20, 2009). 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. What is the probability that a randomly selected worker is both female and employed?"

Answer 1

Answer: 0.42%.

Explanation:

Probability of (M(Eligible Men)) = 0.52

Probability of (W(Eligible Women)) = 1 - 0.52

= 0.48

Probability of (UM(Unemployed Men)) = 0.088

Probability of (UW(Unemployed Women)) = 0.070.

therefore;

Probability that the worker is a man = [P(UM)*P(M)]/[P(UM)*P(M) + P(UW)*P(W)] = 0.576613

0.088 * 0.52 )/ 0.088 * 0.52 + 0.070 * 0.48

= 0.04576 / 0.07936

= 0.5766

probability that the randomly selected worker is both female and unemployed is

= 1 – 0.58%

= 0.42%