Costing for insurance covers

Consider the following situation. In a population of 300 million people, there are two “types” of people. Type H (healthy), and Type S (sick). 90% of the people are healthy (Type H), and have a 1% chance of getting sick. The remainder are Type S and have a 15% chance of getting sick. Getting sick costs $200,000. Type H people are willing to pay $4,000 for insurance that covers their cost of illness. Type S people are willing to pay $22,000 to cover their cost of illness.
a. What is the expected cost of illness for a Type S person? Are they willing to buy insurance?

b. What is the expected cost of illness for a Type H person? Are they willing to buy insurance?

c. What is the expected cost of illness for the population as a whole?

d. If insurance companies could not distinguish who is healthy or who is sick, and can only charge one price for insurance, what would we expect to happen?