People in a certain group have a 0.3% chance of dying this year.If a person in this group buys a life insurance policy for $3,300 that pays $1,000,000 to her family if she dies this year and $0 otherwise,what is the expected value of a policy to the insurance company?
A) $0
B) $300
C) $3,000
D) $3,300

Question

Quizplus · Accepted Answer

The expected value is calculated by multiplying the possible outcomes by their respective probabilities and adding them together. In this case, there are two possible outcomes: the policyholder dies and the insurance company pays out $1,000,000 or the policyholder does not die and the insurance company pays out $0. The probability of the policyholder dying is 0.3%, or 0.003. Therefore, the expected value is:

(0.003 * $1,000,000) + ((1 - 0.003) * $0) = $3,000
The policy is sold for $3,300, so the expected value to the insurance company is negative $300. This means that on average, the insurance company can expect to lose $300 for every policy sold. Therefore, the best choice is B, as it represents the expected value to the insurance company.

People in a Certain Group Have a 0