Question

Suppose a life insurance company sells a ​$230 comma 230,000 ​one-year term life insurance policy to a 19​-year-old female for ​$230. The probability that the female survives the year is 0.999588. Compute and interpret the expected value of this policy to the insurance company.

Answer 1

Probability that the women will survive, p = 0.999588

Probability that the women will not survive, q = 1-p =  1 -0.999588 = 0.000412

Amount gained by the insurance company if the women did survive = $230

Amount lost by the insurance company if the women did not survive = $230 -230000 =-229770

Expected value of the policy for insurance company =

= p*gain +q*lose

= 0.999588*$230 + 0.000412*(-229770)

= $135.24

The expected value of the policy to the insurance company is $281.65