Final answer:
The actuarially fair premium for each group depends on the chances of dying in the next year, considering the presence or absence of a family history of cancer. Charging the actuarially fair premium to the group as a whole may pose challenges for the insurance company.
Step-by-step explanation:
If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group would be calculated based on the chance of dying in the next year for that specific group. In this example, for the group with a family history of cancer, 20% of 1,000 men have a 1 in 50 chance of dying in the next year, so the actuarially fair premium would be calculated accordingly. For the other group without a family history of cancer, 80% of 1,000 men have a 1 in 200 chance of dying in the next year, so the actuarially fair premium for this group would be calculated differently.
If an insurance company were offering life insurance to the entire group without knowing about family cancer histories, the actuarially fair premium for the group as a whole would be calculated based on the overall chances of dying in the next year for the entire group. In this case, the premium would be calculated by considering the combined chances of dying for the group with a family history of cancer and the group without a family history of cancer.
Charging the actuarially fair premium to the group as a whole rather than to each group separately would affect the insurance company's risk assessment and pricing. The insurance company may face challenges in accurately determining the mortality rates and risk profiles of individuals in the group, which could impact the financial viability of the insurance policy.