Suppose you are designing a health insurance policy for a group of $5,000$ young individuals. Their probability of illness is low at $3\%.$ Treating illness is costly though, at $$20,000$ per case.

What is the minimum premium that you would charge each of these $5,000$ individuals for an insurance policy that completely covers their medical expenses in the case of illness?

Will this group of individuals be willing to buy such a policy? Justify your answer.