A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% renteda car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons. What is the probability that a subscriber rented a car during the past 12 months for business or personal reasons (or both)? What is the probability that s subscriber did not rent a car during the past 12 months for either business or personal reasons?

(a) 0.698

(b) 0.302

Step-by-step explanation:

We are given that a survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for both business and personal reasons.

Let Probability that magazine subscribers rented a car during the past 12 months for business reasons = P(BR) = 0.458

Probability that magazine subscribers rented a car during the past 12 months for personal reasons = P(PR) = 0.54

Probability that magazine subscribers rented a car during the past 12 months for both business and personal reasons = = 0.30

(a) Probability that a subscriber rented a car during the past 12 months for business or personal reasons is given by =

As we know that;

So, according to our question;

                                            = 0.458 + 0.54 - 0.30

                                            = 0.998 - 0.30 = 0.698

Hence, probability that a subscriber rented a car during the past 12 months for business or personal reasons (or both) is 0.698.

(b) Probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons = 1 - Probability that a subscriber rented a car during the past 12 months for business or personal reasons

             = 1 -

             = 1 - 0.698 = 0.302

Hence, probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons is 0.302.