Question

There are 100 people in a sport centre.

Answer 1

We need to determinate who doesn't use anything, so first we must know the real number of who are practising: a person can do more things.

For doing this, is better use a three-circles graphic, but we try to do without it.

So

• 16 pool + gym + track, and this number is sure

• 38 gym + pool, but this number includes the people of 1st point. We must know who do only gym + pool: 38 - 16 = 22

• 31 pool + track, this number also includes people of 1st point, so: only pool + track 31 - 16 = 15

• 33 gym + track, this number also includes people of 1st point, so: only gym + track 33 - 16 = 17

now:

• 67 gym, we must know who use only gym: 67 - 16 (gym + pool + track) - 22 (gym + pool) - 17 (gym + track) = 12

• 62 pool, we must know who use only pool: 62 - 16 (gym + pool + track) - 22 (gym + pool) - 15 (pool + track) = 9

• 56 track, we must know who use only track: 56 - 16 (gym + pool + track) - 15 (pool + track) - 17 (gym + track) = 8

now we must now who do some facility: let's sum all

16 + 22 + 15 + 17 + 12 + 9 + 8 = 99

99/100 practise something

So only 1/100 doesn't use nothing

The probability is 1%