A life insurance company sells insurance policies for $50 and the policy pays $1

Question

A life insurance company sells insurance policies for $50 and the policy pays $1,000 if the buyer of the policy dies in the next year. If the company knows the buyer has a 3% chance of dying in the next year, what is the expected value of the policy (to the company)? Don't forget the premium of the policy ($50) is part of the payout. In Problem, note that if only one policy is sold, the company has a 97% chance of profiting from the policy. If 20 policies are sold, what is the probability that the company is profitable from the sales of the policy?

Explanation / Answer

4)

From the given information we have

P(die) = 0.03

P(not die) = 1 - P(die) = 0.97

If the person die the company get $50 - $1000 = -$950

If the person do not die the company get $50

So expected value of the policy for the company is

Expected-value = P(die) *(-950) + P(not die) * ($50) = 0.03 * (-950) + 0.97 * (50) = $20

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