Final answer:
Actuarially fair premium is the amount an insurance company should charge to cover costs and generate profits. Separate premiums would be higher for the group with a family history of cancer. The premium for the whole group would be determined by the overall average risk of death.
Step-by-step explanation:
In the context of life insurance, the term actuarially fair premium refers to the amount of money an insurance company should charge policyholders in order to cover the costs of paying out claims, running the company, and generating profits.
a. 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 than the premium for the group without a family history of cancer. This is because the first group has a higher chance of dying in the next year.
b. If the insurance company were offering life insurance to the entire group without knowing about their family cancer histories, the actuarially fair premium for the group as a whole would be determined by calculating the overall average risk of death among the entire group.