Francesca believes she faces health costs in the current year of either $5,000 with probability 0.8 or $20,000 with probability 0.2.

a. What is the actuarially fair premium for insurance that fully covers health costs Francesca might incur? Explain your answer.

b. Francesca obtains a major medical and hospital policy that covers all costs, aside from a $1,000 annual deductible and a 20% coinsurance rate. If Francesca actually incurs annual health charges of $4,000, by how much will her health insurance company reimburse her?