Question

An insurance policy sells for $600. Based on past data, an average of 1 in 100 policyholders will file a $10,000 claim, an average of 1 in 200 policyholders will file a

$40,000 claim, and an average of 1 in 400 policyholders will file a $60,000 claim. Find the expected value to the company per
policy sold. If the company sells 10,000 policies,
what is the expected profit or loss?
The expected value is?

Answer 1

The expected value to the insurance company per policy sold is $150, and with 10,000 policies sold, the expected profit is $1,500,000.

Step-by-step explanation:

To calculate the expected value to the insurance company for each policy sold, we can use the probabilities and payout amounts given in the question. We multiply the probability of each event by the cost to the company for that event and sum these amounts to get the expected value of a single policy. The expected costs for the company per policyholder are as follows:

• For a $10,000 claim (1 in 100 chance): $10,000 * (1/100) = $100
• For a $40,000 claim (1 in 200 chance): $40,000 * (1/200) = $200
• For a $60,000 claim (1 in 400 chance): $60,000 * (1/400) = $150

The total expected cost per policyholder is the sum of these amounts: $100 + $200 + $150 = $450. However, each policy sells for $600, so the expected profit per policy is the selling price minus the expected cost: $600 - $450 = $150.

With 10,000 policies sold, the total expected profit is 10,000 times the expected profit per policy: 10,000 * $150 = $1,500,000.