A professional organization (for statisticians, of course) sells term life insur

Question

A professional organization (for statisticians, of course) sells term life insurance and major medical insurance. Of those who have just life insurance, 70% will renew next year, and 80% of those with only a major medical policy will renew next year. However,90%ofpolicyholderswhohavebothtypes of policy will renew at least one of them next year. Of the policy holders 75% have term life insurance, 45% have major medical, and 20% have both.

a. Calculate the percentage of policyholders that will renew at least one policy next year.

b. If a randomly selected policy holder does in fact renew next year, what is the probability that he or she has both life and major medical insurance?

Explanation / Answer

P(only term insuarance) =0.75-0.2 =0.55

P(only major medical insurance )= 0.45-0.20=0.25

P(both) =0.20

a)P(renew) =P(only term insuarance and renew)+P(only major medical insurance and renew)+P(both and renew)

=0.55*0.7+0.25*0.8+0.2*0.9=0.765

b) probability that he or she has both life and major medical insurance given policy holder does in fact renew next year =P(both and renew)/P(renew) =0.2*0.9/0.765=0.2353

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