A survey of magazine subscribers shows that 19% rented a car during the past twelve months for business reasons, 52% rented a car during the last twelve months for personal reasons, and 3% rented a car during the last twelve 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?

a. The probability that a subscriber rented a car during the past 12 months for business or personal reasons (P(R)) is given by the probability that they rented a car for business reasons (P(B)=0.19), added to the probability that they rented for personal reasons (P(P)=0.52), subtracted by the probability that they rented for both reasons (P(B and P) = 0.03):

[tex]P(R)=P(B)+P(P)-P(B\cap P)\\P(R) = 0.19+0.52-0.03\\P(R)=0.68[/tex]

b. The probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons (P(N)) is 100% minus the probability that they rented a car (P(R) = 0.68).

[tex]P(N) = 1-P(R) = 1-0.68\\P(N) =0.32[/tex]