Final answer:
The actuarially fair premium for a group with a higher risk would be higher compared to a group with a lower risk. If the insurance company does not know the family cancer histories, the premium would be priced based on an average level of risk for the entire group.
Step-by-step explanation:
In this scenario, the insurance company is selling life insurance to two groups: those with a family history of cancer and those without. The men with a family history of cancer have a higher chance of dying in the next year compared to those without a family history.
If the insurance company were selling life insurance separately to each group, the actuarially fair premium for the group with a family history of cancer would be higher compared to the group without a family history.
This is because the group with a family history has a higher risk of dying, so the premium needs to cover that risk. If the insurance company were offering life insurance to the entire group without knowing their family cancer histories, the actuarially fair premium for the group as a whole would fall somewhere in between the premiums for each individual group.
This is because the group as a whole has a mix of individuals with different risks, and the premium needs to be priced based on an average level of risk.