Venn diagrams for probability

Question

There are 130 people in a sport centre.

61 people use the gym.

68 people use the swimming pool.

60 people use the track.

25 people use the gym and the pool.

30 people use the pool and the track.

19 people use the gym and the track.

6 people use all three facilities.

Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?

Answer 1

13/19 is the probability of G and T but not P

19 ways to get Gym & Track

19-6 are 13 ways to not get the Pool

13/19 = Pr(~P/G^T)