Final answer:
The actuarially fair premium for each group would depend on their mortality rates. Charging a single premium for the entire group without considering family cancer histories would result in adverse selection and potential losses for the insurance company.
Step-by-step explanation:
In this scenario, the insurance company is selling a life insurance policy to two groups of 50-year-old men, those with a family history of cancer and those without. The men with a family history have a higher chance of dying in the next year, while the other group has a lower chance. If the insurance company were selling life insurance separately to each group, the actuarially fair premium for each group would be based on their respective mortality rates. The premium for the group with a family history of cancer would be higher than the premium for the group without a family history.
If the insurance company were offering life insurance to the entire group without knowledge of family cancer histories, the actuarially fair premium for the group as a whole would be calculated based on the weighted average of the mortality rates for the two groups. This premium would fall between the premiums calculated for the separate groups.
If the insurance company tries to charge the actuarially fair premium to the group as a whole rather than to each group separately, it would likely face adverse selection. Adverse selection occurs when individuals with higher risk are more likely to purchase insurance, leading to higher claim payouts for the insurance company. Charging a single premium for the entire group would not adequately account for the differing mortality rates between the two groups and could result in financial losses for the insurance company.