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

Answer:

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

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

Step-by-step 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;

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

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

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