Imagine that 50-year-old men can be divided 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 familyhistory of cancer, and these men have one chance in 50 ofdying in the next year, while the other 80% of men haveone chance in 200 of dying in the next year. The insurance company is selling a policy that will pay $100,000 to theestate of anyone who dies in the next year.
a) If the insurance company were selling life insurance separately to each group, what wouldbe the actuarially fair premium for each group?
b) If an insurance company were offering life insurance to the entire group, but could not findout about family cancer histories, what would be the actuarially fair premium for the group asa whole?
c) What will happen to the insurance company ifit tries to charge the actuarially fair premium tothe group as a whole rather than to each group separately?