A health insurance company charges policyholders a $1250 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $2500. Furthermore, they have estimated that 85% of patients will not be hospitalized, 10% will be hospitalized once a year, and no one will be hospitalized more than twice.
(a) Find the insurance company's expected profit per policyholder.
(b) What is the expected profit if they enroll 80,000 policyholders?