Final answer:
The actuarially fair premium for each group, both with and without a family history of cancer, would be $400,000.
Step-by-step explanation:
For each group, we need to calculate the actuarially fair premium. The actuarially fair premium is the amount of money needed to cover the expected cost of insurance plus any administrative costs and profits for the insurance company.
For the group with a family history of cancer, 20% of 1,000 men (200 men) have a 1 in 50 chance of dying in the next year. Therefore, the expected number of deaths in this group is 200/50 = 4. The expected cost of insurance for this group is $100,000 * 4 = $400,000. So, the actuarially fair premium for this group is $400,000.
For the group without a family history of cancer, 80% of 1,000 men (800 men) have a 1 in 200 chance of dying in the next year. Therefore, the expected number of deaths in this group is 800/200 = 4. The expected cost of insurance for this group is $100,000 * 4 = $400,000. So, the actuarially fair premium for this group is also $400,000.