Question

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

Answer 1

97/125

Explanation:

There are 125 people in a sport centre. 59 people use the gym. = G

70 people use the swimming pool. = P

55 people use the track. = T

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.

A person is selected at random.

What is the probability that this person uses at least 2 facilities?

As illustrated in the Venn diagram,

G' = Gym only

=59-(6+11+19)

=59 - 36=23

P' = Pool only

=70-(6+19+24)

=70-49

=21

T'= Track only

=55-(6+24+11)

=55-31=14

The probability that this person uses at least 2 facilities

= 11+23+19+6+14+24/125

= 97/125