The probability that an 80-year-old male in the U.S. will die within one year is approximately 0.069941. If an insurance company sells a one-year $10,000 life insurance policy to such a person for $495 what is the company's expectation?
The company's expectation can be calculated by multiplying the payout amount by the probability of death and subtracting the cost of the policy.
Expected payout = 10,000 * 0.069941 = $699.41
Company's expectation = Expected payout - Cost of policy = 699.41 - 495 = $204.41
Therefore, the company's expectation is $204.41.
To find the insurance company's expectation, we need to calculate the expected profit or loss from selling the life insurance policy to an 80-year-old male in the U.S.
Step 1: Calculate the expected payout:
The expected payout is the product of the death probability and the insured amount.
Expected payout = 0.069941 * $10,000 = $699.41
Step 2: Calculate the expected revenue:
The expected revenue is the premium amount charged for the policy.
Expected revenue = $495
Step 3: Calculate the expected profit or loss:
Expected profit or loss is the difference between the expected revenue and the expected payout.
Expected profit or loss = Expected revenue - Expected payout
Expected profit or loss = $495 - $699.41
Expected profit or loss = -$204.41
Therefore, the insurance company's expectation for selling a one-year $10,000 life insurance policy to an 80-year-old male in the U.S. is an expected loss of $204.41.