A survey of magazine subscribers showed that 45.1% rented a car during the past

Question

A survey of magazine subscribers showed that 45.1% rented a car during the past 12 months for business reasons, 52% rented a car during the past 12 months for personal reasons, and 20% rented a car during the past 12 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 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?

Explanation / Answer

A:  rented a car during the past 12 months for business reasons

B:  rented a car during the past 12 months for personal reasons

P(A)=0.451

P(B)=0.52

P(A and B)=0.2

a) probability that a subscriber rented a car during the past 12 months for business or personal reasons P(A or B)=P(A)+P(B)-P(A and B)=0.451+0.52-0.2=0.771

b)  probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons is 1-P(A or B)=1-0.771=0.229

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