There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility?

Probability that the person doesn't use any facility = 0.0889

Step-by-step explanation:

Total number of people in a sports center = 135

Number of people using gym 'G' = 73

Number of people using swimming pool 'P' = 59

Number of people using track 'T' = 31

Number of people using gym and pool (G∩P) = 19

Number of people using pool and track (P∩T) = 9

Number of people using gym and track (G∩T) = 16

Number of people using all three facilities (G∩P∩T) = 4

Therefore, from the rule of compound probability,

P(GUPUT) = P(G) + P(P) + P(T) - P(G∩P) - P(G∩T) - P(P∩T) + p(G∩P∩T)

We know probability of an event =

We will plug in the values of probabilities of each event in the formula.

P(GUPUT) =

                 =

                 =

And probability that a person doesn't use any facility = 1 - P(GUPUT)

= 1 -

=

=

= ≈ 0.0889