Respuesta :
Answer:
The correct answer is [tex]\frac{2}{9}[/tex].
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 = [tex]\frac{Favorable}{Total}[/tex] = [tex]\frac{30}{135} = \frac{2}{9}[/tex].
