Question

A life insurance company will sell a 1 million three-year term life insurance policy exclusive in a particular risk group for a premium of ₱2,000.00. Let X denote the net gain to the company from the sale of one policy. If a person in this risk group has a 99.95% chance of surviving within three years, find the expected value to the company of a single policy?

Answer 1

Let $Y$ denote the net gain to the company from the sale of a policy. There are two possibilities,

1. The insured person dies before three years are over.
2. The insured person lives the entire three year period   

wHEN

The probability in the second case is 0.9995 and in the first case, the probability is 1-0.9995=0.0005

The probability distribution of Y is

Y 2000 -998000

p(Y)  0.9995 0.0005

Therefore,

$E(x)=\sum Yp(Y)=2000\times 0.9995+0.0005\times (-998000)=1999-499=1500$

The expected value to the company of a single policy is 1500.