Probabilities -Solution using Set theory & Contingency Table

An insurance company reviews their auto insurance clients and finds the following:

a) all insure at least 1 car
b) 85% insure more than 1 car
C) 23% insure a sports car
d) 17% insure more than 1 car including a sports car

find the probability that a client, selected at random insures only one car and it is NOT a sports car.

Please solve using 1. set theory and 2. Contingency table

(1) n(Insure only one car) = 100 - 85 = 15
n(Insure only one car which is a sports car) = 23 - 17 = 6
n(Insures only one car which is not a sports car) = 15 - 6 = 9
The probability is 9/100 = 0.09

(2) Contingency Table:
Insures more than one car Insures one car Total
Insures a sports car 17 6 23
Does not insure a sports car 68 9 77
Total 85 15 100

The probability is 9/100 = 0.09

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