Question

Suppose a life insurance company sells a

​$180 comma 000180,000

​one-year term life insurance policy to a

2222​-year-old

female for

​$280280.

The probability that the female survives the year is

0.9995450.999545.

Compute and interpret the expected value of this policy to the insurance company.

The expected value is

​$nothing.

Answer 1

Probability that the female survives the year, p = 0.999545

Probability that the female do not survives the year, q = 1-0.999545 = 0.000455

Loss to the company if the female do not survive = 280- $180000 = - $179720

Gain to the company if the female survive = $280

Expected value = p*gain + q*lose

= 0.999545*280 + 0.000455*(-179720)

= $198.1

The insurance company expects to earn an average profit of $198.1 on 22 year old female.