Question

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 accompanying 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 0.07 (7% of all such individuals). Auto 0.05 0.20 0.15 Suppose an individual having both types of policies is randomly selected. 0.04 0.07 0.02 0.07 0.10 0.03 0.04 0.08 0.15 (a) What is the probability that the individual has a medium auto deductible and a high homeowners deductible? (b) What is the probability that the individual has a low auto deductible? What is the probability that the individual has a low homeowner's deductible? (c) What is the probability that the individual is in the same category for both auto and homeowner's deductibles? (d) Based on your answer in part (c), what is the probability that the two categories are different? (e) What is the probability that the individual has at least one low deductible level? (f) Using the answer in part (e), what is the probability that neither deductible level is low?

Answer 1

a) P(medium auto and high homeowner's) = 0.08

b) P(low auto deductible) = 0.04 + 0.07 + 0.05 + 0.04 = 0.2

   P(low homeowner's deductible) = 0.07 + 0.10 + 0.03 = 0.2

c) P(both auto and homeowner's deductible) = 0.07 + 0.2 + 0.15 = 0.42

d) P(the two categories are different) = 1 - 0.42 = 0.58

e) P(at least one low deductible level) = 0.04 + 0.07 + 0.05 + 0.04 + 0.10 + 0.03 = 0.33

f) P(neither deductible is low) = 1 - 0.33 = 0.67