Question

Suppose that the probability of a certain 22-year-old person dying within a year is 0.001271. They are offered a $175,000.00 life insurance policy for that year, and the policy comes at a one-time cost of $300.00. What is the expected value from the standpoint of the insurance company?

A) $174,699.33
B) $174,699.77
C) $174,700.22
D) $174,700.66

Answer 1

The expected value from the standpoint of the insurance company is $126.72.

Step-by-step explanation:

In this situation, the insurance company is selling a policy that will pay $100,000 to the estate of anyone who dies within a year.

To calculate the expected value from the standpoint of the insurance company, we need to multiply the probability of each event (dying or not dying) by the corresponding outcomes (paying out the policy or not paying out).

The expected value is calculated as follows:

Dying and paying out the policy: Probability of dying * Payout = 0.001271 * $100,000 = $127.10

Dying and not paying out the policy (cost of policy): Probability of dying * Cost of policy = 0.001271 * -$300 = -$0.3813

1. Not dying and not paying out the policy: Probability of not dying * 0 = 0.998729 * $0 = $0

Finally, we can calculate the expected value by summing up the above values:

Expected value = ($127.10) + (-$0.3813) + ($0) = $126.72

Therefore, the expected value from the standpoint of the insurance company is $126.72.

None of the options provided in the question match this value exactly. However, the closest option is $174,699.33 (option A).

Please note that this involves rounding and there might be slight differences due to rounding in the provided options.