Question

There are 135 people in a sport centre. 73 people use the gym. 73 people use the swimming pool. 67 people use the track. 36 people use the gym and the pool. 35 people use the pool and the track. 32 people use the gym and the track. 14 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

Perfectly suited for a Venn diagram setup

Start with the intersection of 14, fill in that data in the intersection of all 3 circles that you must have drawn.

Now look at the intersection of any two circles:
I will pick the gym and track circles, it says that 36 use both of those
but the 14 from the intersection is included in that count, so 22 would go
in the part describing ONLY gym and track, so put 22 in that region.
Continue with the other two intersection of two circles

Now look at each of the whole circles.
e.g. the gym circle, it says that 73 use the gym.
Obviously that would include all those data values that you already
entered in the "gym" circle. So subtract those values form 73 and enter
the rest in the "gym only" part of the circle.
Continue for the other two circles.

Now add up all those values in the circles. If that total is less than 135
then the difference would go outside the 3 circles.

Your prob is that number / 135