An insurance company sells different types of policies, including auto and homeo
ID: 3241325 • Letter: A
Question
An insurance company sells different types of policies, including auto and homeowners policies. 60% of customers have auto policies, 40% have homeowners policies, and 20% have both types. The remaining customers have other types of policies. a. What percent of customers have only auto policies. Only homeowners policies? In the past, 60% of customers with only auto policies renewed them after one year. For those with only homeowners policies 70% renewed, and for those with both types, 80% renewed. b. If we randomly select a customer with either an auto or homeowner policy, or both, what is the probability that he or she will renew?Explanation / Answer
customers have auto policies = 60%
customers have homewoners policies = 40%
customers have both types policies = 20%
(a) customers have only auto policies = 60% - 20% = 40%
customers have only homeowners policies = 40% - 20% = 20%
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customers have other types of policies = 100% - 40% - 20% - 20% = 20%
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(b) suppose total customers = 100
customers have only auto policies = 40
customers have only homewoner policies = 20
customers have both type of policies = 20
60% of customers with only auto policiesrenewed i.e. 40*60% = 24 customers
70% of customers with only auto policiesrenewed i.e. 20*70% = 14 customers
80% of customers with only auto policiesrenewed i.e. 20*80% = 16 customers
total number of customer of auto, homewoners and both policies = 40 + 20 + 20 = 80
total number of customers renewed = 24 + 14 + 16 = 44
therefore, if we select randomly a customer with either an auto of homewoner policy, or both, the probablity that he or she will renew = 44 / 80 = 0.55
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