Final answer:
Actuarially fair premiums are set so that individuals pay amounts reflecting their risk. For a group of 50-year-old men, premiums would vary if family history of cancer is known. Charging a uniform premium to the entire group might lead to losses for the insurer if not balanced by risk.
Step-by-step explanation:
When discussing actuarially fair premiums, we're looking at a method to determine the fair price of insurance based on the risk each person presents. In terms of health insurance, an actuarially fair premium is calculated such that the amount paid by an individual is proportional to their expected healthcare costs. This reflects their risk to the insurer. For instance, people with chronic diseases or the elderly usually pose a higher risk due to their increased healthcare needs and, consequently, they would face higher premiums.
For the group of 50-year-old men segmented into those with a family history of cancer and those without, calculating an actuarially fair premium would consider each subgroup's risk of dying within the next year. The expected number of deaths in the group with a family history of cancer (20% of 1,000, with a 1 in 50 chance) and the group without (80% of 1,000, with a 1 in 200 chance) would be multiplied by the policy payout ($100,000), defining the cost that the insurer expects to cover. Consequently, premiums would be adjusted accordingly to reflect these costs.