Final answer:
Actuarially fair premiums are calculated based on the risk of each group. A single premium for a whole group without considering cancer history would lead to an average rate. Charging such a rate to everyone could cause adverse selection, where high-risk individuals are more likely to buy the insurance, potentially leading to financial losses for the insurer.
Step-by-step explanation:
If the insurance company were selling life insurance separately to each group, the actuarially fair premium can be calculated by considering the probability of each event and the payout associated with it. For the group with a family history of cancer (20% of 1,000 men with a 1 in 50 chance of dying within the next year), the premium would reflect the higher risk.
Conversely, the group without a family history of cancer (80% of 1,000 men with a 1 in 200 chance of dying) would have a lower premium due to the lower risk.
When calculating the actuarially fair premium for the group as a whole, without distinction of cancer history, the insurer would average the risk across the entire population, resulting in a single premium that is higher than that for the low-risk group but lower than that for the high-risk group.
Should the insurance company charge the actuarially fair premium to the group as a whole, it may lead to adverse selection, where high-risk individuals are more likely to buy the insurance while low-risk individuals opt out, finding it unfair or too expensive. This could potentially destabilize the insurance pool and result in financial losses for the company.