Question

An insurance policy sells for ​$800. Based on past​ data, an average of 1 in 50 policyholders will file a ​$15,000 ​claim, an average of 1 in 100 policyholders will file a

​$30,000 ​claim, and an average of 1 in 400 policyholders will file ​a $70,000 claim. Find the expected value​ (to the​ company) per policy sold. If the company sells 20,000​policies, what is the expected profit or​ loss?

The expected value is ​$____
The profit is $_____

Answer 1

The expected value is $375

The profit is $6,500,000

Explanation:

Amount of claim:

15000, 30000, 70000

Probability:

1/100, 1/200, 1/400

So the expected value of the claim is:

15000 × (1/100) + 30000 × (1/200) + 70000 × (1/400) = 475

Given that an insurance policy sells for $800 and the expected value of the claim is $475.

So, the expected value of the companies profit is = $(800 – 475) = $325.

If the company sells 20,000 policies then the expected profit is = $(20000 × 325) = $6,500,000

Thus, The expected value (to the company) per policy sold is $375 and the expected profit is $6,500,000.

-TheUnknownScientist 72