Final answer:
The actuarially fair premium for each group with separate insurance policies would be $25,000. If insurance is offered to the entire group without knowledge of family cancer histories, the actuarially fair premium for the group as a whole would be $14,285.71. Charging the actuarially fair premium to the group as a whole could lead to adverse selection for the insurance company.
Step-by-step explanation:
Insurance Premiums and Risk Groups
To determine the actuarially fair premium for each group, we need to calculate the expected claims for each group and divide it by the number of people in that group. For the group with a family history of cancer, 20% of 1,000 men (200 men) have a 1 in 50 chance of dying, so the expected claims for this group is 200/50 = 4. For the other group, 80% of 1,000 men (800 men) have a 1 in 200 chance of dying, so the expected claims for this group is 800/200 = 4. Therefore, the actuarially fair premium for each group is $100,000/4 = $25,000.
If the insurance company were offering life insurance to the entire group without knowing the family cancer histories, they would calculate the average chance of dying for the entire group. The average chance of dying for the entire group is (20% * 1/50) + (80% * 1/200) = 0.005 + 0.002 = 0.007. Therefore, the actuarially fair premium for the group as a whole would be $100,000/0.007 = $14,285.71.
If the insurance company tries to charge the actuarially fair premium to the group as a whole, it will face adverse selection. People with a family history of cancer will be more likely to purchase insurance because they would be getting a good deal compared to the premium they would pay if they were in a separate risk group. This would result in higher claims for the insurance company and could lead to financial losses.