A survey of magazine subscribers shows that 20% rented a car during the past twe

Question

A survey of magazine subscribers shows that 20% rented a car during the past twelve months for business reasons, 40% rented a car during the last twelve months for personal reasons, and 6% 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 for business reasons, given that she rented one for personal reasons?

b) Given that she rented one for business reasons, what is the probability that a subscriber rented a car for personal reasons?

Explanation / Answer

P(business reason) = 0.2

P(personal reason) = 0.4

P(business and personal reason) = 0.06

A) P(business reason | personal reason) = P(business reason and personal reason) / P(personal reason)

= 0.06 / 0.4

= 0.15

B) P(personal reason | business reason) = P(personal reason and business reason) / P(business reason)

= 0.06 / 0.2

= 0.3

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