Final answer:
If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group would be $4,000. If the insurance company were offering life insurance to the entire group as a whole without considering family cancer histories, the actuarially fair premium for the group as a whole would also be $4,000. If the insurance company tries to charge the actuarially fair premium to the group as a whole, it may face challenges such as adverse selection.
Step-by-step explanation:
If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group can be calculated using the formula:
Premium = (Number of people in the group * Probability of dying) * Policy amount / 1 year
Therefore, the actuarially fair premium for this group would be:
(200 * (1/50) * 100,000) / 1 year = $4,000
Similarly, for the group without a family history of cancer:
The actuarially fair premium for this group would be:
(800 * (1/200) * 100,000) / 1 year = $4,000
If the insurance company were offering life insurance to the entire group as a whole without considering family cancer histories, the actuarially fair premium for the group would be the weighted average of the premiums for each group:
Actuarially fair premium for the group as a whole = (Premium for the group with a family cancer history * Percentage of people with a family cancer history) + (Premium for the group without a family cancer history * Percentage of people without a family cancer history)
Actuarially fair premium for the group as a whole = (4,000 * 0.2) + (4,000 * 0.8) = $4,000
If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than to each group separately, it may face some challenges. This is because the premium may not accurately reflect the risk associated with each group. Those with a family history of cancer may be at a higher risk compared to those without a family history of cancer, but the premium would be the same. This could result in adverse selection, where those with a higher risk are more likely to purchase the insurance policy, leading to potential financial losses for the insurance company.