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. (Round your answers to 2 decimal places.)

a. What is the probability that a randomly selected woman in that age group is married or is participating in the labor force?

p =

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?

p =

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

p =

Explanation / Answer

a)

probability that a randomly selected woman in that age group is married or is participating in the labor force

p=P(participated)+P(married)-P(participated and married)=0.75+0.78-0.61=0.92

b)

probability that a randomly selected woman in that age group is married or is participating in the labor force but not both =P(married or is participating)-P(participated and married) =0.92-0.61=0.31

c)

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

=1-P(married or is participating) =1-0.92 =0.08

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