Question 24 page 397 Chapter 16.(Principles of Microeconomics) book

Imagine that you can divide 50 year old men into two groups: those who have a family history of cancer and those who do not. For the purposes of this example, say that 20% of a group of 1,000 men have a family history of cancer, and these men have one chance of 50 of dying in the next year, while the other 80% of men have one chance in 200 of dying in the next year. The insurance company is selling a policy that will pay $100,000 to the estate of anyone who dies in the next year.

If the insurance company were selling life insurance separately to each group, what would be the actuarially fair premium for each group?

If an insurance company were offering life insurance to the entire group, but could not find out about family cancer histories, what would be the actuarially fair premium for the group as a whole?

What will happen to the insurance company if it tries to charge the actuarially farm premium to the group as a whole rather than to each group separately? Include in your answer a full explanation as to who purchase the insurance and who does not.