SOLUTION: The probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941. If an insurance company sells a one-year, $11,000 life insurance policy to

Question 1132897: The probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941. If an insurance company sells a one-year, $11,000 life insurance policy to such a person for $482, what is the company's expectation?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the probability that the person will die in 1 year is .069941.
the price of the policy is 482 dollars.
if the person dies within the year, the insurance company is out 11,000.

the expected value to the insurance company is 482 - .069941 * 11000 = -287.351.

one way to look at this is to assume they sell a certain number of such policies to 80 years old males.

let's say they sell 1,000,000 of them.
.069941 * 1,000,000 = 69,941 will die within a year of when they purchased the policy if the probability holds.
the company makes 1,000,000 * 482 = 482,000,000 dollars from them.
the company loses 69,941 * 11,000 = 769,351,000 dollars on the ones who have died within the year.
the net loss to the company is 769,351,000 - 482,000,000 = 287,351,000 dollars.
divide that by 1,000,000 and it comes out to be an average loss of 287.351 dollars for each policy sold.

that doesn't sound like a good deal for the company.
it looks like they charged too little.

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