Final answer:
In an insurance policy scenario where 20% of 1,000 50-year-old men have a higher mortality rate due to a family history of cancer, an insurer may expect to pay out $400,000 for each subgroup (with and without a history), totaling $800,000.
Step-by-step explanation:
Understanding Insurance Policy Payouts Based on Mortality Rates
When examining a hypothetical group of 1,000 50-year-old men in relation to insurance policies, we can leverage statistical analysis to understand insurance payouts. With 20% having a family history of cancer and a 1 in 50 mortality rate within a year, and the remaining 80% having a 1 in 200 mortality rate, an insurance company selling a policy with a $100,000 payout upon death faces different risks for each subgroup.
For the subgroup with a family history of cancer:
- Number of men: 200 (20% of 1,000)
- Mortality risk: 1 in 50
- Expected deaths: 4 (200 divided by 50)
- Total expected payout: $400,000 (4 multiplied by $100,000)
For the subgroup without a family history of cancer:
- Number of men: 800 (80% of 1,000)
- Mortality risk: 1 in 200
- Expected deaths: 4 (800 divided by 200)
- Total expected payout: $400,000 (4 multiplied by $100,000)
Total expected payout for the entire group would therefore be $800,000, which is the sum of the expected payouts from each subgroup.