Question

A survey of magazine subscribers showed that rented a car during the past months for business reasons, rented a car during the past months for personal reasons, and rented a car during the past months for both business and personal reasons. Round your answers to three decimal places. a. What is the probability that a subscriber rented a car during the past months for business or personal reasons? b. What is the probability that a subscriber did not rent a car during the past months for either business or personal reasons?

Answer 1

`P(business\ or\ personal) = 69.8\%`

`P(Not(business\ or\ personal)) = 30.2\%`

Explanation:

The question has missing details; however, the giving parameters are:

`P(business) = 45.8\%`

`P(personal) = 54\%`

`P(both) = 30\%`

Solving (a): Business or Personal

This is calculated as follows:

`P(business\ or\ personal) = P(business) + P(personal) - P(both)`

`P(business\ or\ personal) = 45.8\% + 54\% - 30\%`

`P(business\ or\ personal) = 69.8\%`

Solving (b): Not business or personal

This is calculated using complements of probability;

`P(Not(business\ or\ personal)) = 1 - P(business\ or\ personal)`

`P(Not(business\ or\ personal)) = 1 - 69.8\%`

`P(Not(business\ or\ personal)) = 30.2\%`