An insurance company offers four different deductible levels for its homewowner\

Question

An insurance company offers four different deductible levels for its homewowner's policyholders: none, low, medium, high. There are three different deductible levels for its automobile policyholders: low medium, high. The company wants to analyze its customers that have both automobile and home policies. The accompanying table gives proportions for the various categories of policyholders who have both types of insurance Homeowner's Auto N L MFH 0.04 0.06 0.05 0.03 M 0.07 01 0.2 0.1 H 0.02 0.03 0.15 0.15 Suppose an individual with both policies is selected at random (a) What is the probability that the individual has a medium auto deductible and a high homeowner's (b) What is the probability that the individual has a medium auto deductible or a high homeowner's (c) What is the probability that the individual does not have an auto policy that is in the same (d) Given that the individual has a low auto policy, what is the probability that their homeowner's deductible? deductible? deductible category as their homeowner's policy? policy is also low?

Explanation / Answer

from given table:

a) P( medium auto deductible & high homeowner's deductible) =0.1

b) P(medium auto deductible or high homeowner's deductible) =(0.07+0.1+0.2+0.1+0.03+0.15)=0.65

c)P(not have auto policy in same deductible category as homeowner's policy) =1-P(both are in same category)

=1-(0.06+0.2+0.15)=0.59

d) P(low  homeowner's policy|low auto policy) =P(low  homeowner's policy & low auto policy)/P(low auto plicy)

=0.06/0.18 =1/3 =0.3333

( please revert for any clrification required)

Homeowner Auto N L M H Total L 0.04 0.06 0.05 0.03 0.18 M 0.07 0.1 0.2 0.1 0.47 H 0.02 0.03 0.15 0.15 0.35 Total 0.13 0.19 0.4 0.28 1

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