Question

There are 130 people in a sport centre.
73 people use the gym.
62 people use the swimming pool.
58 people use the track.
22 people use the gym and the pool.
29 people use the pool and the track.
25 people use the gym and the track.
11 people use all three facilities.
A person is selected at random.
What is the probability that the person uses exactly one of the facilities?

Answer 1

The probability that the person uses exactly one of the facilities = 95/130 .

What is Probability ?

Probability is the branch of Mathematics which helps to determine the likeliness of an event to happen.

The data is given and the probability that the person uses exactly one of the facilities is asked

73 people use the gym. P(G)

62 people use the swimming pool. P (S)

58 people use the track. P (T)

22 people use the gym and the pool. P (G ∩ P)

29 people use the pool and the track. P (P ∩ T)

25 people use the gym and the track. P (G ∩ T)

11 people use all three facilities. P (P∩G∩T)

P (PUGUT) = P(G) + P (S) + P (T) - P (G ∩ P) - P (P ∩ T) - P (G ∩ T) - 2 P (P∩G∩T)

73 + 62 + 58 -22-29-25 -11-11 = 95

The probability that the person uses exactly one of the facilities = 95/130 .

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