Question

There are 120 people in a sport centre.

78 people use the gym.
46 people use the swimming pool.
45 people use the track.
21 people use the gym and the pool.
16 people use the pool and the track.
24 people use the gym and the track.
9 people use all three facilities.
Given that a randomly selected person uses the gym and the track, what is the probability they do not use the swimming pool?

Answer 1

The probability that a randomly selected person who uses the gym and the track does not use the swimming pool is 5/8.

Step-by-step explanation:

To solve this problem, we need to calculate the conditional probability that a person uses the gym and the track but does not use the swimming pool. This can be accomplished with the help of Venn Diagrams or formula, but since we have all the needed information, we can calculate it directly.

We are told that 24 people use both the gym and the track. Furthermore, 9 people use all three facilities. To find out how many people use just the gym and the track, we subtract the ones that also use the pool: 24 people - 9 people = 15 people.

Therefore, there are 15 people who use the gym and the track but not the swimming pool. To find the probability, we divide the 15 people by the total number of people that use the gym and the track, which is 24.

The probability is therefore 15/24, which simplifies to 5/8. This is the probability that a randomly selected person who uses the gym and the track does not use the swimming pool.