The U.S. Bureau of Labor Statistics publishes data on the benefits offered by sm
ID: 3245888 • 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 31% 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.)
**(Round your answers to 2 decimal places.)
A) *
B) *
C) **
D) **
E) *
Explanation / Answer
The company offers retirement plans =42%
so, P(R) =0.42
The company offers life insurance =61%
so, P(I) = 0.61
The company offers retirement plan and insurance =31%
so, P(RI) =0.31
a) Probability of company offers a retirement plan given that they offers a life insurance
P(R/L) =P(RI)/P(I) =0.31/0.61=0.5082
b) Probability of company offers life insurance given that they offers a retirement plan
P(L/R) = P(RI)/P(R) =0.31/0.42 =0.7381
c) Probability of company offers insurance or retirement plan
P(IUR) = P(I) +P(R)- P(RI) =0.61+0.42 -0.31 =0.72
d) Probability of company offers a retirement plan and does not offers life insurance
P(R) –P(RI) =0.42- 0.31 =0.11
e) Probability of company does not offer life insurance if it is known that offer a retirement plan
[P(R) – P(RI)] /P(R) =0.11/0.42 =0.2620
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