what is the company's expectation?

Question

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, $12,000 life insurance policy to such a person for $435, what is the company's expectation? (Round your answer to two decimal places.)

Answer 1

The expected value is the sum of the probabilities of an outcome multiplied by value.

In this example, the company will either pay out the 12,000 or not --or insured will die or not in the time frame

If the insured dies, they will pay 12,000 while taking in $435, so net outcome is a loss of $11,565

If the insured survives, the company realizes income of $435

The expected value is:

-11,565 (0.069941) + 435 (1-0.069941) = -808.87 + 404.58 = -404.29

They would expect to lose $404.29