Data from the Bureau of Labor Statistics indicates that in a certain month. 32.4

Question

Data from the Bureau of Labor Statistics indicates that in a certain month. 32.4% of the labor force had a high school diploma or fewer years of education, 28.2% had some college or an associate's degree, and 39.4% had a bachelor's degree or more education. Of those with a high school diploma or fewer years of education, 7.6% were unemployed. Of those with some college or an associate's degree. 5.5% were unemployed, and of those with a bachelor's degree or more education, 5.1% were unemployed. Find the probability that a randomly chosen labor force participant has a bachelor's degree or more education given that he or she is employed. The probability is (Type an integer or decimal rounded to three decimal places as needed.)

Explanation / Answer

Ans:

P(diploma or fewer)=0.324

P(college degree)=0.282

P(dgree or more education)=0.394

P(unemployed/diploma or fewer)=0.076

P(unemployed/college degree)=0.055

P(unemployed/degree or more education)=0.051

P(unemployed)=0.324*0.076+0.282*0.055+0.394*0.051=0.060228

P(employed)=1-0.060228=0.939772

Using Bayes theorm:

P(degree or more education/employed)=P(degree or more education and employed)/P(employed)

=P(employed/degree or more education)*P(degree or more education)/P(employed)

=((1-0.051)*0.394)/0.939772

=(0.949*0.394)/0.939772

=0.398

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