There are 125 people in a sport centre. 59 people use the gym. 70 people use the swimming pool. 55 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 17 people use the gym and the track. 6 people use all three facilities. Given that a randomly selected person uses the gym and the track, what is the probability they use all the facilities?

Answer:97/125

Step-by-step explanation:

"As illustrated in the Venn diagram,

We let

U=[The total number of people at the sport center]

This implies that,

n (U) = 125

G=[Those who use the gym]

This implies that,

n (G) = 59

P=[Those who use the pool]

This implies that,

n (P) = 70

T=[Those who use the track]

This implies that,

n (T) = 55

a=[Those who use the gym only]

This implies that,

n (a) = 59 - (6+11+19) = 59-36=23

b=[Those who use the pool only]

This implies that,

n (b) = 70 - (6+19+24) = 70-49=21

c=[Those who use the track only]

This implies that,

n (c) = 55 - (6+24+11) = 55-31=14

Also, number of people who use gym and track=11+23+19+6+14+24=97"

The answer is 97/125