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 homeowner policy will renew next year.
The company estimates that 80%of policyholders who have both an auto and a homeowner 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 homeowner policy,and 15%of policyholders have both an auto and a homeowner policy.Using the company's estimates,what is the percentage of policyholders that will renew at least one policy next year?
A.20%
B.29%
C.41%
D.53%
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Answer:D
Explanation:Let:
A=event that a policyholder has an auto policy
H=event that a policyholder has a homeowners policy Then,based on the information given:
Therefore,the proportion of policyholders that will renew at least one policy is shown below:
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