Final answer:
Actuarially fair premiums for life insurance depending on risk factors are calculated as $2,000 for those with a family history of cancer and $500 for those without. Combining the groups leads to an $800 premium per person, but this could result in adverse selection if lower-risk individuals opt out, jeopardizing the insurance policy's sustainability.
Step-by-step explanation:
The question pertains to the calculation of actuarially fair premiums for life insurance policies given different risk factors, specifically a family history of cancer. To calculate the premiums:
- For the group with a family history of cancer, the probability of dying within the next year is 1 in 50. Assuming there are 200 men in this category (20% of 1,000), the expected payout would be 200 men × (1/50) × $100,000 = $400,000. Dividing this amount by the number of men gives an actuarially fair premium of $400,000 / 200 = $2,000 per person.
- For the group without a family history of cancer, the probability of dying within the next year is 1 in 200. With 800 men in this group (80% of 1,000), the expected payout would be 800 men × (1/200) × $100,000 = $400,000. This leads to a premium of $400,000 / 800 = $500 per person.
- If the insurance company offers a policy to the entire group without differentiating between the two risk levels, the actuarially fair premium across the entire group would incorporate the overall risk. The total expected payout would be $800,000 for the 1,000 men, leading to a premium of $800 per person.
If the insurance company charges the group premium rather than individual premiums based on risk, individuals with a lower risk might choose not to buy the insurance as they would be subsidizing the higher risk group, resulting in adverse selection that could make the policy unsustainable for the insurance company.