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

Explanation:

Given that :

U = 130

Let :

s = swimming pool

t = track

g = gym

n(g) = 61 ; n(s) = 68 ; n(t) = 60

n(g n s) = 25 ; n(t n s) = 30 ; n(g n t) = 19

n(g n s n t) = 6

n(g n t) only = n(g n t) - n(g n s n t) = 19 - 6 = 13

Hence, probability that a randomly scted person uses the gym and track and does not use the swimming pool = n(g n t) only ÷ n(g n t)

= 13 / 19

= 13 / 19