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 $485, what is the company's expectation? (Round your answer to two decimal places.)
The company's expectation is equal to the expected value of the insurance policy.
The expected value of the insurance policy is calculated by multiplying the probability of an event occurring by the amount of money associated with that event. In this case, the event is the 80-year-old male dying within one year, and the associated amount of money is $10,000.
So, the company's expectation is equal to:
0.069941 * $10,000 = $699.41
Therefore, the company's expectation is $699.41.
To calculate the insurance company's expectation, we need to multiply the probability of death within one year by the amount the company pays out in the event of death, and then subtract the premium paid by the insured.
The amount the insurance company pays out in the event of death is $10,000.
The probability of death within one year is 0.069941.
The premium paid by the insured is $485.
Therefore, the expectation is calculated as follows:
Expectation = (Probability of Death * Payout) - Premium
= (0.069941 * $10,000) - $485
= $699.41 - $485
= $214.41
So, the insurance company's expectation is $214.41.