An actuary at an insurance company estimates from existing data that on a $1,000 policy, an average of 1 in 100 policyholders will file a $20,000 claim, an average of 1 in 200 policyholders will file a $50,000 claim, and an average of 1 in 500 policyholders will file a $100,000 claim.
a. What is the expected value to the company for each policy sold?
b. If the company sells 100,000 policies, can it expect a profit? Explain the assumptions of this calculation.