The U.S. Bureau of Labor Statistics publishes data on the benefits offered by sm
ID: 3173509 • Letter: T
Question
The U.S. Bureau of Labor Statistics publishes data on the benefits offered by small companies to their employees. Only 42% offer retirement plans while 61% offer life insurance. Suppose 36% offer both retirement plans and life insurance as benefits. If a small company is randomly selected, determine the following probabilties:
a. The company offers a retirement plan given that they offer life insurance.
b. The company offers life insurance given that they offer a retirement plan.
c. The company offers life insurance or a retirement plan.
d. The company offers a retirement plan and does not offer life insurance.
e. The company does not offer life insurance if it is known that they offer a retirement plan.
Explanation / Answer
P(Retirement plan) = 0.42
P(Life insurance) = 0.61
P(Both) = 0.36
a) P(Retirement plan | Life insurance)
= P(Both) / P(Life insurance)
= 0.36/ 0.61
= 0.5902
b) P(Life insurance | Retirement plan)
= P(Both) / P(Retirement plan)
= 0.36/ 0.42
= 0.8571
c) P(Life insurance or retirement plan)
= P(Life insurance) + P(Retirement plan) - P(Both)
= 0.61 + 0.42 - 0.36
= 0.67
d) P(Retirement plan but not life insurance)
= P(Retirement plan) - P(Both)
= 0.42 - 0.36
= 0.06
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