Question

A survey of magazine subscribers showed that 45.9% rented a car during the past 12 months for business reasons, 53% rented a car during the past 12 months for personal reasons, and 29% rented a car during the past 12 months for both business and personal reasons.

(a)

What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons?

(b)

What is the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons?

Answer 1

Solution:
Given in the question
P(Business reasons) = 0.459
P(Personal Reasons) = 0.53
P(Business and Personal Reasons) = 0.29
Solution(a)
In this question, we need to calculate probability that a subscriber rented a car during the past 12 months for business or personal reasons
P(Business or Personal reason) = P(Business) + P(Personal) - P(Business and Persnal) = 0.459 + 0.53 - 0.29 = 0.699
So there is 69.9% probability that a subscriber rented a car during the past 12 months for business or personal reasons.
Solution(b)
In this question, we need to calculate the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons which can be calculated as
P(Business or Personal reason)' = 1 - P(Business or Personal reason)= 1 - 0.699 = 0.301
So there is 30.1% probability that the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons.