Question

Fill in the Blanks.

Acasa Insurance Company offers two plans for home insurance. Plan A has a $750 yearly premium with a $3,000 deductible. Plan B has a $1,200 yearly premium with a $1,000 deductible. Last year, 20% of all policyholders made damage claims. The average claim amount was $6,500.

The expected value per claim for every customer who chooses plan B is $______
. The expected value per claim for every customer who chooses plan A is $______
.

Answer 1

The expected value per claim for Plan B is $1,100, considering a $1,200 premium and a $1,000 deductible. For Plan A, with a $750 premium and a $3,000 deductible, the expected value per claim is $700. These values are based on the probability of a claim being made and the average payout after deductibles.

Step-by-step explanation:

The expected value per claim for customers who choose either plan can be calculated by considering the probability of making a claim and the average payout after the deductible is applied. Since 20% of all policyholders make claims, and the average claim amount is $6,500, we can calculate the expected value for both Plan A and Plan B.

For Plan B with a $1,000 deductible, the insurance will pay out $6,500 - $1,000 = $5,500 on average per claim. Given that only 20% of policyholders make claims, the expected value per claim for Plan B is 20% of $5,500, which is $1,100.

For Plan A with a $3,000 deductible, the insurance pays out $6,500 - $3,000 = $3,500 on average per claim. Therefore, the expected value per claim for Plan A is 20% of $3,500, which is $700.

Finally, the correct statement is: The expected value per claim for every customer who chooses plan B is $1100. The expected value per claim for every customer who chooses plan A is $700.