5. An insurance company offers four different deductible levels none, low, mediu

Question

5. An insurance company offers four different deductible levels none, low, medium, and high for its homeowner's policyholders and three different levels - low, medium, and high - for its automobile policyholders. The following table gives proportions for the various categories of policyholders who have both types of insurance. For example, the proportion of individuals with both low homeowner's deductible and low auto deductible is 0.06 (6% of all such individuals). Auto Low Medium High None 0.04 0.07 0.02 Homeowner's Low 0.06 0.10 0.03 Medium 0.05 0.20 0.03 0.10 0.15 Suppose an individual having both types of policies is randomly selected. (a) What is the probability that the individual has a medium auto deductible and a (b) What is the probability that the individual has a low auto deductible? A low (c) What is the probability that the individual is in the same category for both (d) Based on your answer in part (c). what is the probability that the two (c) What is the probability that the individual has at least one low deductible () Based on your answer in part (d), what is the probability that neither high homeowner's deductible? homeowner's deductible? auto and homeowner's deductible? categories are different? level? deductible level is low?

Explanation / Answer

Solution- (a) Probability that the individual has a medium auto deductible and a high homeowner's deductible = .1

(2nd row , 4th column)

(b) Probability of low auto deductible = .04 + .06 + .05 + .03 = .18

Probability of low homeowners deductible = .06 + .1 + .03 = .19

(c) Probability that category is same for both auto and homeowners deductible = .06 + .2 + .15

= .41

(d) Probability that two categories are different = 1 -.41

= .59

(e) Probability of atleast one low deductible = .04 + .06 + .05 + .03 +.1 + .03

=.31

(f) probability that neither is low = 1-.3

= .69

TY!

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