# 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 !. set theory and 2. Contingency table

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

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

Â© BrainMass Inc. brainmass.com December 24, 2021, 8:07 pm ad1c9bdddf>https://brainmass.com/statistics/contingency-table/probabilities-solution-using-set-theory-contingency-table-249909