Data from the Bureau of Labor Statistics indicates that in a certain month, 33.5

Question

Data from the Bureau of Labor Statistics indicates that in a certain month, 33.533.5% of the labor force had a high school diploma or fewer years of education, 23.323.3% had some college or an associate's degree, and 43.243.2% had a bachelor's degree or more education.  Of those with a high school diploma or fewer years of education, 6.66.6% were unemployed.  Of those with some college or an associate's degree, 6.56.5% were unemployed, and of those with a bachelor's degree or more education, 2.22.2% were unemployed.  Find the probability that a randomly chosen labor force participant has a bachelor's degree or more educationa bachelor's degree or more education given that he or she is employedemployed. The probability is

Explanation / Answer

P(A | B) = P(A and B) / P(B)

P(bachelor's degree or more education | employed) = P(bachelor's degree or more education and employed) / P(employed)

P(bachelor's degree or more education and employed) = 0.432x(1-0.022) = 0.4225

P(employed) = 0.335x(1-0.066) + 0.233x(1-0.065) + 0.432x(1-0.022) = 0.9532

So, P(bachelor's degree or more education | employed) = 0.4225/0.9532 = 0.4432

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