Suppose that 70% of the population is generally healthy and 30% of the population is unhealthy. There is a 20% chance that a person gets sick whether they are healthy or unhealthy. However, their health status does affect the costs of their illness. The cost associated with an illness for a healthy person is $600, but for an unhealthy person, it is $10,000. (Note: insurance companies cannot distinguish healthy from unhealthy individuals in advance). Consider the expenses of an illness, either $600 or $10,000. The insurance company makes no expected profits, in expectation, it charges premiums to cover its expected costs. Let's assume that both healthy and unhealthy people are risk-neutral.

Question: If only unhealthy people buy the insurance, what would be the actuarially fair premium? Please show your calculations.