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Please help I don't can't figure out the answer

There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track 19 people use the gym and the pool. 9 people use the pool and the track 16 people use the gym and the track, 4 people use all three facilities. Given that a randomly selected person uses at least two facilities, what is the probability they use all the facilities?​

Sagot :

Answer:

1/9

Step-by-step explanation:

4 people use all three facilities, then

16 - 4 = 12 people use the gym and the track and do not use the pool;

9 - 4 = 5 people use the pool and the track and do not use the gym;

19 - 4 = 15 people use the gym and the pool and do not use the track.

At least two facilities use 4 + 12 + 5 + 15 = 36 people, 4 of them use all three facilities. Thus, the probability that a randomly selected person which uses at least two facilities, uses all the facilities is 4/36

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