There are 135 people in a sport centre. 73 people use the gym. 73 people use the swimming pool 67 people use the track 36 people use the gym and the pool. 35 people use the pool and the track 32 people use the gym and the track 14 people use all three facilities. How many people didn't use any facilities?
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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
\dfrac{4}{36}=\dfrac{1}{9}364=91
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