A 28-year-old man pays $192 for a one-year life insurance policy with coverage of $150,000. If the probability that he will live through the year is 0.9989, what is the expected value for the insurance policy?

I have not done actuarial science, but I would be tempted to calculate it as

192/(1-0.9989)=$174,545.
I wonder how the number 0.9989 was calculated.

To find the expected value for the insurance policy, we need to calculate the product of the payout amount and the probability of receiving that payout.

In this scenario, the payout amount is $150,000, and the probability of the insured living through the year is 0.9989. The probability of the insured dying during the year would then be 1 - 0.9989 = 0.0011.

To calculate the expected value, we multiply the payout amount by the corresponding probabilities and sum them up:

Expected value = (Payout amount * Probability of payout) + (Payout amount * Probability of no payout)

Expected value = ($150,000 * 0.9989) + ($0 * 0.0011)

Since the insured will receive the payout if he lives through the year and $0 if he dies, we can simplify the equation as follows:

Expected value = $150,000 * 0.9989

Expected value = $149,835

Therefore, the expected value for the insurance policy is $149,835.