The U.S. Bureau of Labor Statistics publishes data on the benefits offered by sm

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 33% 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.

*(Round your answers to 4 decimal places.)

Explanation / Answer

here let event  retirement plans are R ;  life insurance =L

hence from above P(R) =0.42 ; P(L) =0.61 ; P(R n L) =0.33

a) P(company offers a retirement plan given that they offer life insurance) =P(R|L) =0.33/0.61=0.5410

b)P(company offers life insurance given that they offer a retirement plan)=P(L|R) =0.33/0.42 =0.7857

c)P(company offers life insurance or a retirement plan) =P(R)+P(L)-P(R n L) =0.42+0.61-0.33=0.7

d) P( company offers a retirement plan and does not offer life insurance) =P(R)-P(R n L) =0.42-0.33=0.09

e)  P(company does not offer life insurance if it is known that they offer a retirement plan)=1-P(L|R) =1-0.7857

=0.2143

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