Final answer:
The expected value of the $100,000 term life insurance policy for the insurance company for one year, based on the given probabilities, is $67.05. This is calculated by the profits when the insured survives (probability 0.9962) minus the loss if the insured passes away (probability 0.0038).
Step-by-step explanation:
The question involves finding the expected value of a term life insurance policy for an insurance company. This is done by calculating the weighted average of possible outcomes, taking into account the probabilities of these outcomes.
To find the expected value, we consider two scenarios for the insurance company with regard to the 55-year-old woman who has bought a $100,000 policy. The first scenario is if the woman survives the year, in which case the company profits by the amount of the annual payment she made, which is $456. The probability of this scenario is 0.9962. The second scenario is if the woman passes away during the year, and the company has to pay out $100,000. The probability of this happening is 1 - 0.9962 = 0.0038.
The expected value (EV) of the insurance policy is calculated as follows:
EV = (Probability of surviving * Profit when surviving) + (Probability of passing away * Loss when passing away)
EV = (0.9962 * $456) - (0.0038 * $100,000)
EV = $447.05 - $380
EV = $67.05
Therefore, the expected value of the policy for the insurance company for one year is $67.05.