We will use the example above and interpret this as health insurance. Suppose there are 100 people: 95 people will be healthy and 5 will be sick, but at the time the insurance is purchased, no one knows who will be sick. Assume purchase of insurance is mandatory. If you are healthy, you incur no health costs. If you become sick, you incur costs of $115. The total health expenses for the 5 people will equal $575 (so 5 times 115). If all 100 people split the cost of the illness, what is the insurance premium paid by each person? Show that this payment is equal to the probability of illness times the cost per person, or the expected value of health costs for an individual.

An important part of the statement of the problem was the assumption insurance purchase is mandatory. Suppose that insurance purchase is not mandatory and there is a no pre-condition clause, meaning you cannot be denied insurance coverage because of a pre-condition. Explain how the absence of mandatory insurance plus the no pre-condition clause leads to an adverse selection problem.

Please show the result with calculation. I will report you if you copy and past standard definitions from the test book.