Question

Statistics help, please.
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 ..(continue on comments)

Answer 1

calculate the percentage of policyholders that will renew at least one policy next year.
Options:
20
29
53
70

Answer 2

This is a trick question!
When you add up the percentage of clients, you get 65+50+15=130% which is impossible.
However, when we realize that the 15% is included in both the 65% (auto) and 50% (home) policies, then things will make sense.
So we have
auto=65-15=50%
home=50-15=35%
both=15%
Total = 50+35+15=100%
Can you finish the rest, using law of total probabilities?

Answer 3

I got it. Thanks @mathmate