An insurance company estimates that 40% of policyholders who have only an auto policy will renew next year and 60% of policyholders who have only a homeowners policy will renew next year. The company estimates that 80% of policyholders who have both an auto and a homeowners policy will renew at least one of those policies next year.
Company records show that 65% of policyholders have an auto policy, 50% of policyholders have a homeowners policy, and 15% of policyholders have both an auto and a homeowners policy.
Using the company’s estimates, calculate the percentage of policyholders that will renew at least one policy next year.
- 20
- 29
- 41
- 53 Correct Answer
- 70
Solution: D
Let
Then based on the information given,
and the portion of policyholders that will renew at least one policy is given by
