Question

There are 130 people in a sport centre. 65 people use the gym. 51 people use the swimming pool. 44 people use the track. 15 people use the gym and the pool. 14 people use the pool and the track. 10 people use the gym and the track. 1 person uses all three facilities. A person is selected at random. What is the probability that this person uses at least 2 facilities?

Answer 1

0.285

Explanation:

Total peoples are, n=130

Number of people who use gym =65

Number of people who use swimming pool =51

Number of people who use the track =44

Number of people who use the gym and the pool =15

Number of people who use the pool and the track =14

Number of people who use the gym and the track =10

Number of people who use the gym, the pool, and the track =1

So, the number of people who use the gym and the pool =15-1=14

The number of people who use the pool and the track =14-1=13

The number of people who use the gym and the track =10-1=9

Now, the people who use at least two facilities are the people who use 2 or 3 facilities, which is 14+13+9+1=37.

So, the number of favorable outcomes =37

Total number of sample space, n=130

Hence, the probability, P, that the 1 randomly selected person uses at least 2 facilities is as follows:

`P=(37)/(130)=0.285`