Question

There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
Given that a randomly selected person uses at least two facilities, what is the probability they
use all the facilities?

Answer 1

Answer:

$\dfrac{1}{9}$

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

$\dfrac{4}{36}=\dfrac{1}{9}$