Question

An insurance company charges $900 annually for auto policies for teenagers. The policy specifies that the company will pay $1500 for a minor accident and $8000 for a major accident. If the probability of a teenager having a minor accident during a given year is 0.15, and of having a major accident is 0.05, how much can the insurance company expect to make on 10 policies?

Answer 1

The insurance company can expect to make an expected earnings of $2750 from 10 auto policies for teenagers, considering the given probabilities and payouts for minor and major accidents.

Step-by-step explanation:

The student is asking about expected earnings from auto insurance policies for an insurance company. Using the provided probabilities and payment amounts, we can calculate the expected payout for a policy, and then determine the expected revenue from 10 policies. The insurance company charges $900 per policy. With a probability of 0.15 for a minor accident, the expected payout is $1500 x 0.15 = $225. For a major accident, with a probability of 0.05, the expected payout is $8000 x 0.05 = $400. Therefore, the total expected payout per policy is $225 + $400 = $625.

For 10 policies, the total expected payout is $625 x 10 = $6250. As the total income from 10 policies is $900 x 10 = $9000, the expected earnings for the company from 10 policies would be $9000 - $6250 = $2750.