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According to Labor Statistics, 75% of the women 25 through 49 years of age participate in the Labor force. Suppose 78% of the women in that age group are married. Suppose also that 61% of all women 25-49 years of age are married and are participating in the labor force. a. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force?

b. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force but not both?

c. What is the probability that a randomly selected woman in that age group is neither married nor participating in the labor force?

Janet S.
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1 Answers1

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Let A = the event that a woman randomly selected participate in labor force, and B = the event that a woman randomly selected is married, and ~X = complement of X.

a. P(A or B) = P(A) + P(B) - P(A and B) = .75 + .78 - .61 = .92

b. P[(A and ~B) or (B and ~A)] = P(A and ~B) + P(B and ~A) = P(A) - P(A and B) + P(B) - P(B and A) = .75 - .61 + .78 - .61 = .14 + .17 = .31

c. P(~A and ~B) = P(~(A or B)) = 1 - P(A or B) = 1 - .92 = .08

DeepSea
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