Question

An insurance policy sells for 800. Based on past data, an average of 1 in 125 policyholders will file a 15,000 claim, an average of 1 in 250 policyholders will file a 50,000 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?

Answer 1

The expected value per policy for the company is $330. For 10,000 policies sold, the total expected profit is $3,300,000.

To calculate the expected value per policy to the insurance company, we account for the probability and cost of the claims. The probability of a $15,000 claim is 1/125, the probability of a $50,000 claim is 1/250, and the probability of a $60,000 claim is 1/400. We multiply these probabilities by their respective claim amounts and sum them to calculate the expected loss per policy. The revenue from each policy is $800.

The expected loss per policy is (1/125)*$15,000 + (1/250)*$50,000 + (1/400)*$60,000 = $120 + $200 + $150 = $470. Therefore, the expected value per policy for the company is $800 - $470 = $330.

With 10,000 policies sold, the expected total profit is 10,000 * $330 = $3,300,000.

So, the expected profit per policy is $330, and the total expected profit from selling 10,000 policies is $3.3 million.