Question

- There are 130 people in a sport centre,

76 people use the gym,
60 people use the swimming pool,
32 people use the track,
23 people use the gym and the pool.
8 people use the pool and the track
20 people use the gym and the track,
6 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

0.6462 = 64.62% probability that the person uses exactly one of the facilities

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

20 people use the gym and the track and 6 people use all three facilities

So 20-6 = 14 use exactly the gym and the track and 6 use all three.

8 people use the pool and the track

So 8 - 6 = 2 use exactly the pool and the track.

23 people use the gym and the pool.

So 23 - 6 = 17 use exactly the gym and the pool.

32 people use the track

So 32 - (6 + 14 + 2) = 10 use only the track.

60 people use the swimming pool

So 60 - (6 + 2 + 17) = 35 use only the pool.

76 people use the gym

So 76 - (6 + 14 + 17) = 39 use only the gym

What is the probability that the person uses exactly one of the facilities?

Out of 130, 39 + 35 + 10 = 84 use exactly one of the facilities.

84/130 = 0.6462

0.6462 = 64.62% probability that the person uses exactly one of the facilities