Expected Value for Life Insurance There is a 0.9986 probability that a randomly selected 30-year-old male lives through the year (based on data from the U.S. Department of Health and Human Services). A Fidelity life insurance company charges \(161 for insuring that the male will live through the year. If the male does not survive the year, the policy pays out \)100,000 as a death benefit.

a. From the perspective of the 30-year-old male, what are the monetary values corresponding to the two events of surviving the year and not surviving?

b. If a 30-year-old male purchases the policy, what is his expected value?

c. Can the insurance company expect to make a profit from many such policies? Why?

The probability ofa 30-year old male living through the year is equal to 0.9986.

The insurance company charges $161 for one year and gives $100,000 on the death of a man.

a.

The monetary value of the event of surviving through the year is equal to -$161 as the charges of the insurance policy need to be paid.

Corresponding to the event of not surviving, any particular man will receive $100,000.

Therefore, the corresponding monetary value is equal to

$100,000-161=99,839\text{dollars}$

Thus, the monetary value for the event of not surviving is equal to $99,839.

b.

The expected value of purchasing the insurance policy is computed as follows.

$$\begin{gathered} \text{Expected}\text{value}=\left(\text{Net}\text{amount} \\ \text{received}\right)\times \left(\text{Probability}\text{of} \\ \text{not}\text{surviving}\right)-\left(\text{Net}\text{amount} \\ \text{given} \\ \right)\times \left(\text{Probability} \\ \text{of}\text{surviving}\right) \\ =\left(99839\right)\left(1-0.9986\right)-\left(161\right)\left(0.9986\right) \\ =-21\text{dollars} \end{gathered}$$

Thus, the expected value of purchasing an insurance policy is equal to -21 dollars.

c.

For each policy sold, the insurance company earns 21 dollars.

Therefore, the insurance company makes a lot of profit by selling many such policies.