An insurance company sells different types of policies, including auto and homeo

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

Ans:

a)P(only autopolicies)=0.6-0.2=0.4

P(only homeowner policies)=0.4-0.2=0.2

P(having both auto policies and homeoner policies)=0.2

b)

P(renewed having only autopolicies)=0.6*0.4=0.24

P(renewed having only homeowner policies)=0.7*0.2=0.14

P(renewed having both auto policies and homeoner policies)=0.8*0.2=0.16

P(renewed/having an auto or homeowner policy or both)=(0.24+0.14+0.16)/(0.4+0.2+0.2)=0.54/0.8=0.675

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