Question

There are 130 people in a sport centre. 73 people use the gym. 62 people use the swimming pool. 58 people use the track. 22 people use the gym and the pool. 29 people use the pool and the track. 25 people use the gym and the track. 11 people use all three facilities. A person is selected at random. What is the probability that this person doesn't use any facility

Answer 1

To find : Probability that person doesn't use any facility

Given : Total people = 130 ; People using gym (G), Swimming Pool (S), Track (T) = 73, 62, 58 respectively. People using G & P, P & T, G & T = 22, 29, 25. People using P & G & T = 11

So : Prob (G) = 73/ 130 , Prob (S) = 62/130 , Prob (T) = 58/130

P (G ∩ P) = 22 / 130 , P (P ∩ T) = 29 / 130 , P (G ∩ T) = 25 / 130 , P (P ∩ G ∩ T) = 11 / 130

Prob [ Person uses either P or G or T ] :

P (PUGUT) = P(G) + P (S) + P (T) - P (G ∩ P) - P (P ∩ T) - P (G ∩ T) - 2 P (P∩G∩T) = ( 73 + 62 + 58 - 22 - 29 - 25 - 22) / 130 = 95 / 130

Prob [Person uses neither P or G or T] : 1 - Pr [Person uses either  P or G or T] = 1 - P (PUGUT) = 1 - (95 / 130) = 35 / 130

Hence, Probability that person doesn't use any facility = 35 / 130

To learn more, refer https://brainly.com/question/17089724?referrer=searchResults