Question

There are 135 people in a sport centre. 77 people use the gym. 62 people use the swimming pool. 65 people use the track. 27 people use the gym and the pool. 23 people use the pool and the track. 31 people use the gym and the track. 4 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

Answer:

The correct answer is $\frac{2}{9}$.

Step-by-step explanation:

There are 135 people in a sport centre.

Let the experiment be to pick a person from the sport centre who only uses exactly one of the facilities.

Total number of possible outcomes = 135

For the gym:

77 people use the gym.

27 people use the gym and the pool.

31 people use the gym and the track.

4 people use all three facilities.

Total number of people using only the gym are 77 - ( 27 + 31 + 4) = 15

For the swimming pool:

62 people use the swimming pool.

27 people use the gym and the pool.

23 people use the pool and the track.

4 people use all three facilities.

Total number of people using only the swimming pool are 62 - ( 27 + 23 + 4) = 8

For the tracks:

65 people use the track.

23 people use the pool and the track.

31 people use the gym and the track.

4 people use all three facilities.

Total number of people using only the tracks are 65 - ( 23 + 31 + 4) = 7

A person is selected at random.

Favorable outcomes = 7 + 8 + 15 = 30

Probability that the person uses exactly one of the facilities = $\frac{Favorable}{Total}$ = $\frac{30}{135} = \frac{2}{9}$.