6. An insurance company estimatest renew next year and 60% of policyholders who

Question

6. An insurance company estimatest 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 policy holders have an auto policy, 50% of policyholders have a homeowners policy and 15 % of policy holders have both an auto and a homeowners policy. Using the company's estimate, calculate the percentage of policyholders that will renew at least one policy next year.

Explanation / Answer

% of policy holders that will renew at least one policy =P(only auto policy and renew+only home policy and renew+both policy and renew)=(0.65-0.15)*0.4+(0.5-0.15)*0.6+0.15*0.8=0.53 ~53%

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