Question

An insurance policy sells for ​ $ 8 0 0 . Based on past ​ data, an average of 1 in 1 2 5 policyholders will file a ​ $ 2 0 , 0 0 0 ​ claim , an average of 1 in 2 0 0 policyholders will file a ​ $ 4 0 , 0 0 0 ​ claim , and an average of 1 in 5 0 0 policyholders will file ​ $ 7 0 , 0 0 0 claim. Find the expected value ​ ( to the ​ company ) per policy sold. If the company sells 2 0 , 0 0 0 ​ policies , what is the expected profit or ​ loss?

Answer 1

The expected value to the insurance company per policy sold is $300, and if the company sells 20,000 policies, the expected profit is $6,000,000.

Step-by-step explanation:

The question is asking for help to calculate the expected value for an insurance company per policy sold and expected profit or loss if 20,000 policies are sold.

The insurance sells policies for $800, and there are probabilities of claims of different amounts that need to be factored into the expected value calculation.

To find the expected value per policy, we calculate it by taking the sum of all possible values of claims, each multiplied by the probability of that claim occurring. The calculation is:

1. For the $20,000 claim: 1/125 chance, the expected value is $20,000 * (1/125) = $160.
2. For the $40,000 claim: 1/200 chance, the expected value is $40,000 * (1/200) = $200.
3. For the $70,000 claim: 1/500 chance, the expected value is $70,000 * (1/500) = $140.

The total expected value of claims is $160 + $200 + $140 = $500.

Since the policy sells for $800, the expected profit per policy is $800 - $500 = $300.

To find the expected profit for 20,000 policies, we simply multiply the expected profit per policy by the number of policies, so the expected profit is $300 * 20,000 = $6,000,000.