Question

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

The probability that a subscriber rented a car during the past 12 months for business or personal reasons is 0.698 or 69.8%. The probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons is 0.302 or 30.2%.

Step-by-step explanation:

To find the probability that a subscriber rented a car during the past 12 months for business or personal reasons, we can use the formula:

P(Business or Personal) = P(Business) + P(Personal) - P(Business and Personal)

Substituting the given values, we have:

P(Business or Personal) = 0.458 + 0.54 - 0.3 = 0.698

Therefore, the probability that a subscriber rented a car during the past 12 months for business or personal reasons is 0.698 or 69.8%.

To find the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons, we can subtract the probability of renting a car from 1:

P(Not Renting) = 1 - P(Business or Personal)

Substituting the given value, we have:

P(Not Renting) = 1 - 0.698 = 0.302

Therefore, the probability that a subscriber did not rent a car during the past 12 months for either business or personal reasons is 0.302 or 30.2%.