Company life probability

Question

11 percent of a certain company's life insurance policy holders are smokers. For each nonsmoker the probability of dying during the year is 0.009. For each smoker the probability of dying during the year is 0.04. 

Find the probability that a policy holder who died last year was a smoker. 

Answer 1

From Bayes Law: P(s|D) = P(D|s)P(s)/P(D) where s means person is a smoker, and D means the person died. and | means "given that".

P(D|s) = .04 P(s) = .11 and P(D) = P(D|s)P(s) + P(D|~s)P(~s) = .11(.04) + (.89)(.009) = .01241

P(D|s) = .0044/.01241 = .355 or 35.5%

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