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. A person is selected at random. What is the probability that this person uses at least 2 facilities?

Answer 1

9514 1404 393

Answer:

  43/120 ≈ 0.3583

Step-by-step explanation:

Adding up the folks who use two facilities counts the folks who use all three 3 times. So, the number who use two or more facilities is ...

  21 +16 +24 -2(9) = 43 . . . . people who use 2 or more facilities

The probability that a person chosen randomly from the 120 at the sports center uses at least 2 facilities is ...

 43/120 ≈ 0.3583

_____

The given numbers add up as follows:

  Gym only: 42

  Pool only: 18

  Track only: 14

  Gym and Pool only: 12

  Gym and Track only: 15

  Pool and Track only: 7

  Gym and Pool and Track: 9

  No facilities: 3