Final answer:
The actuarially fair premiums are calculated by determining the expected payouts based on mortality rates for different groups and dividing by the number of people in each group. Charging the entire group a single premium could lead to adverse selection, as higher-risk individuals would be more likely to buy insurance, while lower-risk individuals might forgo it.
Step-by-step explanation:
The student's question is about calculating the actuarially fair premiums for life insurance policies based on mortality rates for two different groups of 50-year-old men, taking into account their family history of cancer. By definition, an actuarially fair premium is one that equals the expected payout for the insurance policy.
For the group with a family history of cancer representing 20% of 1,000 men, we calculate the expected payout by multiplying the probability of dying (1 in 50) by the number of men in this subgroup (200 men) and finally by the sum insured ($100,000). For the group without a family history of cancer, we do the same using their respective risk of dying (1 in 200) and group size (800 men).
Actuarially fair premiums would be the total expected payouts divided by the number of men in each subgroup. When considering the entire group without distinguishing based on family history, we calculate a blended risk by adding the individual expected losses for each subgroup and then dividing by the total number of men (1,000).
If the insurance company charges the actuarially fair premium calculated for the entire group, without separating the groups based on risk, it may face issues related to adverse selection. Higher-risk individuals will be more inclined to purchase insurance, while lower-risk individuals may opt not to, degrading the risk pool and potentially leading to financial losses for the insurer.