Final answer:
Actuarially fair premiums vary based on individual risk factors. For two groups of men differentiated by family cancer history, the premiums are calculated separately based on their respective risk of death. Charging the entire group a blended rate without distinguishing risk could result in adverse selection and financial losses for the insurer.
Step-by-step explanation:
When considering how to price life insurance premiums, actuaries must calculate the actuarially fair premium based on the risk profile of the group or individual. To calculate the fair premium for each group separately:
- For the 20% with a family history of cancer (200 individuals), with a 1 in 50 chance of dying in the next year, the premium would be the probability of death multiplied by the payout: (1/50) * $100,000 = $2,000.
- For the 80% without a family history of cancer (800 individuals), with a 1 in 200 chance of dying, the premium would be (1/200) * $100,000 = $500.
To calculate the premium for the entire group without knowledge of family cancer history, the probability of death for each subgroup is weighted by its representation in the overall population:
((200 * 1/50) + (800 * 1/200)) / 1,000 * $100,000 = $600.
Therefore, the actuarially fair premium for the entire group would be $600.
If the insurance company charges this blended rate to the whole group, adverse selection may occur. The lower-risk group may opt out, finding the premium too high relative to their risk, leaving the insurance company with a pool of higher-risk individuals, potentially leading to losses.