Probability Q

Question

A company sells a certain insurance policy that has a maximum payout of 30k when a customer makes a claim.Suppose that, each year,2% of the customers receive the full claim of 30k, 3% receives a claim of 20k, not more than 5% receives a claim of 10k, while the rest of the customers do not submit a claim. What is the minimum amount the policy should be charged in order not to make a loss.

Answer 1

You want Expected Value = Payment - [0.02(30,000) + 0.03(20,000) + 0.05(10,000) + 0.9(0)] to be zero (or more, if you're a good businessman).  Solve!