Both Shirley and Emma are applying to insure their car against theft. Shirley lives in a secure neighborhood, where the probability of theft is 10%. Emma lives in a lesser secure neighborhood where the probability of theft is 30%. Both Shirley and Emma own cars worth $20,000, and are willing to pay $500 over expected loss for insurance.
Suppose the insurance company cannot tell them apart but expects them to be different values and charges them an average premium of $4,500. How much profit would it make?