please show work Problem 7 Fifty-six percent of all American workers have a comp

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please show work

Problem 7 Fifty-six percent of all American workers have a company sponsored re tirement plan, 68% have health insurance and 49% have both benefits. If a worker is selected at random: a) What is the probability that the worker has neither a company sponsored retirement plan n or health insurance? b) What is the probability that the worker has health insurance if he has a retirement plan? c) Are having health insurance and a retirement plan independent events? Explain your answer. d) Are having the two benefits mutually exclusive? Explain your answer

Explanation / Answer

Let RP represents retirement plan and HB represents helath benefits.

a) P(RP or HB) = P(RP) + P(HB) - P(RP and HB) = 0.56 + 0.68 - 0.49 = 0.75

Hence,

P(Neither) = 1 - 0.75 = 0.25

b) P(HB | RP) = P(HB and RP)/ P(RP) = 0.49/0.56 = 7/8 = 0.875

c) No these are not independent events because:

P(HB | RP) is not equal to P(HB).

d)n No they aren't mutually exclusive because a worker can have both the things at the same time.

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