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There is a 0.9986 probability that a randomly selected 30 year old male lives through the year (based on data from the US department of Health and Human Services). A Fidelity life insurance company charges $161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out $100,000 as a death benefit. If a 30 year old male purchases the policy, what is his expected value?

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Answer:

a) Surviving the year: $ -161. Not surviving: 99,839.

b) 0.9986 * -161 + (1-0.9986) * 100000 = -20.7746

c) As the expected value is negative from the male's perspective, it is positive from the insurance company's perspective. So as the number of people purchasing this insurance becomes large, the company's profit will converge to an average value of 20.7746 per male. So the company is indeed profitting.

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