推 AAJJBurnett:3Q~ 10/04 11:54
※ 編輯: AAswallow 來自: 218.164.78.169 (10/04 12:45)
※ 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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