Final answer:
The actuarially fair premium for different groups can be calculated based on the probabilities of different outcomes and their corresponding payouts.
Step-by-step explanation:
The actuarially fair premium is the premium that covers the expected payout of an insurance policy. To calculate the actuarially fair premium, we need to consider the probabilities of different outcomes and their corresponding payouts.
a. If the insurance company were selling life insurance separately to each group, the actuarially fair premium for the group with a family history of cancer would be (20% * 1000 * 1/50 * $100,000), and for the group without a family history of cancer, it would be (80% * 1000 * 1/200 * $100,000).
b. If the insurance company couldn't find out about family cancer histories and was offering life insurance to the entire group, the actuarially fair premium for the group as a whole would be (1000 * 1/100 * $100,000).
c. If the insurance company tried to charge the actuarially fair premium to the group as a whole instead of each group separately, it would be at a disadvantage because it would overcharge the low-risk group and undercharge the high-risk group.