An insurance company o?ers four di?erent deductible levels - None, Low, Medium,

Question

An insurance company o?ers four di?erent deductible levels - None, Low, Medium, and High for its homeowner’s policyholders, and three di?erent levels - Low, Medium, High - for its automobile policyholders. The company gathered data and the table below has been constructed.

Suppose an individual is randomly selected, what is the likelihood that the individual has

b. a medium auto deductible and no homeowner deductible? Are these two events independent? Verify.

c. a low homeowner deductible or a high auto deductible?

d. no homeowner deductible given that the individual has a medium auto deductible?

Homeowner Policy Auto Policy None Low Medium High Total 125 120 115 360 3551468 Low 150 130 130 110 115 118 130535 Medium 110470 115 463 High Total 395 358 3

Explanation / Answer

b)P(medium auto deductible and no home owner deductible)=130/1468=0.0886

as P(medium auto deductible)*P(home owner deductible)=(470/1468)*(395/1468)=0.0861

as P(medium auto deductible)*P(home owner deductible) is not equal to P(medium auto deductible and no home owner deductible) ; they are not independent.,

c)

P(a low homeowner deductible or a high auto deductible)=(358+463-118)/1468=0.4789

d)

P(no homeowner deductible given that the individual has a medium auto deductible)=130/470=0.2766

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