According to the U.S. Bureau of Labor Statistics, 75% of the women 25 through 49

Question

According to the U.S. Bureau of 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 women 25 through 49 years of age are married and are participating in the labor force. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force? 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? is the probability selected woman in that age group is neither married nor participating in the labor force?

Explanation / Answer

Let A= the event that a woman randomly selected participate in labour force

B= the event tha awoman randomly selected is married

and ~X = compliment of X

P(A)= .75 , P(B) = .78 , P(A and B) = .61

a. the probability that a randomly selected woman in that age group is married or is participating in labour force,

P(A or B) = P(A) + P(B) - P(A and B)

               = .75 + .78 -.61 = .92 (answer)

b. the probability that arandomly selected woman in that age group is married or is participating in labour force but not both , P(A and ~B) or P(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 (answer)

c. the probability that arandomly selected woman in that age group is neither married nor participating in the labour force P(~A and ~B)

=P(~(A or B))

=1- P(A or B)

= 1- .92

=.08 (answer)

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