An insurance company calculates the probability that a man with a Type A lifesty

Question

An insurance company calculates the probability that a man with a Type A lifestyle will be alive in the next thirty years is 0.7. the probability that a man with a Type B lifestyle survives the next 30 years is 0.9. The life span of one type man has no impact on the life span of the other type of man. (A Venn Diagram may help, but it is not crucial to the problem). a. What is the probability that both men will be alive in the next 30 years? b. What is the probability that at least one will be alive in the next thirty years? c. What is the probability that only one will be alive after the next thirty years? d. What is the probability that neither will be alive in thirty years? e. What is the probability that the Type A man doesn't survive the next thirty years given the Type B man does?

Explanation / Answer

Both events are indepedent,

a) P(Type A and Type B alive) = 0.7*0.9 = 0.63

b) P(at least one alive) = P(A and B alive) + P(A alive and B not alive) + P(A not alive and B alive)
= 0.63 + 0.7*0.1 + 0.3*0.9 = 0.97

c) P(only one alive) = P(A alive and B not alive) + P(A not alive and B alive) = 0.7*0.1 + 0.3*0.9 = 0.34

d) P(neither alive) = P(A not alive and B not alive) = 0.3*0.1 = 0.03

e) P(A not alive| B alive) = P(A not alive) = 1 - 0.7 = 0.3(since the events are independent)

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