The probability that a 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 $485, what is the company’s expectation?
To calculate the insurance company's expectation, we need to multiply the probability of the event occurring (the person dying) by the amount the company receives (the premium) and subtract the amount the company pays out (the face value of the policy).
Exp = (Probability of event) * (Amount received) - (Amount paid out)
Given:
Probability of event = 0.069941
Amount received = $485
Amount paid out = $10,000
Exp = 0.069941 * $485 - $10,000
Exp = $33.98 - $10,000
Exp = -$9,966.02
The insurance company's expectation is -$9,966.02. This means that, on average, the insurance company can expect to lose nearly $9,966 when they sell this life insurance policy to an 80-year-old male in the U.S.
To calculate the insurance company's expectation, we need to multiply the probability of the insured individual dying within one year by the amount the insurance company will pay if that happens.
Step 1: Calculate the expected payout if the insured individual dies within one year.
Expected payout = Probability of death * Total payout
Expected payout = 0.069941 * $10,000
Expected payout = $699.41
Step 2: Subtract the premium paid by the insured individual from the expected payout.
Expectation = Expected payout - Premium
Expectation = $699.41 - $485
Expectation = $214.41
Therefore, the insurance company's expectation is $214.41.