※ 引述《AAJJBurnett (叫我投手)》之銘言： : A life insurance company issues standard,preferred,and ultra-preferred : policies.Of the company's policyholders of a certain age ,60% are standard : with a probability of 0.01 of dying in the next year ,30% preferred with a : probability of 0.08 of dying in the next year, and 10% are ultra-preferred : with a probability of 0.07 of dying in the next year .A policyholder of : that age dies in the next year .What are the conditional probabilities : of the deceased being standard,preferred,and ultra-preferred ? There are three type of policies issued by a life insurance company. Let X1、X2、X3 are the events of policyholders buying standard, preferred, and ultra-preferred, respectively. Besides, let Y is the event of policyholders dying in the next year. So P(X1) = 0.6、P(X2) = 0.3、P(X3) = 0.1 P(Y|X1) = 0.01、P(Y|X2) = 0.08、P(Y|X3) = 0.07 Given the policyholder dies in the next year, the conditional probabilities of the deceased being standard, preferred, and ultra-preferred are P(X1|Y), P(X2|Y), and P(X3|Y), respectively. P(Y) = P(X1)P(Y|X1) + P(X2)P(Y|X2) + P(X3)P(Y|X3) = 0.0307 P(X1|Y) = P(X1∩Y)/P(Y) = 0.1954 P(X2|Y) = P(X2∩Y)/P(Y) = 0.7818 P(X3|Y) = P(X3∩Y)/P(Y) = 0.0228 # --

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