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Jonathan would like to visit one of the 12 gyms in his area.

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Jonathan would like to visit one of the 12 gyms in his area.

by Anaira Mitch » Mon Jan 09, 2017 7:35 pm
Jonathan would like to visit one of the 12 gyms in his area. If he selects a gym at random, what is the probability that the gym will have both a swimming pool and a squash court?
(1) All but 2 gyms in the area have a squash court.
(2) Each of the 9 gyms with a pool has a squash court.

Please help with this problem.
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by Jay@ManhattanReview » Mon Jan 09, 2017 11:01 pm
Anaira Mitch wrote:Jonathan would like to visit one of the 12 gyms in his area. If he selects a gym at random, what is the probability that the gym will have both a swimming pool and a squash court?
(1) All but 2 gyms in the area have a squash court.
(2) Each of the 9 gyms with a pool has a squash court.

Please help with this problem.
The probability that the gym will have both a swimming pool and a squash court = (Number of gyms that have both a swimming pool and a squash court)/12

We have to get the number of gyms that have both a swimming pool and a squash court.

S1: The statement implies that 10 gyms have squash court while 2 do not. We have no information about the number of gyms with pools. Insufficient.

S2: The statement implies that 'Number of gyms that have both a swimming pool and a squash court' = 9.

Thus, the probability that the gym will have both a swimming pool and a squash court = 9/12 = 3/4. Sufficient.

Answer: B

-Jay
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