Question

There are 130 people in a sport centre. 61 people use the gym. 68 people use the swimming pool. 60 people use the track. 25 people use the gym and the pool. 30 people use the pool and the track. 19 people use the gym and the track. 6 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?

Answer 1

Answer:

$\frac{59}{130}$

Explanation:

As shown in the Venn diagram,

Let

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

This implies that

n(U)=130

G=[Those who use the gym]

This implies that

n(G)=61

P=[Those who use the pool]

This implies that

n(P)=68

T=[Those who use the track]

This implies that

n(T)=60

a=those who use only the gym

b=those who use only the pool

c=those who use only the track

From the digram,

a=61-(13+6+19)=61-38=23

b=68-(6+24+19)=68-49=19

c=60-(13+6+24)=60-43=17

The number of people who use exactly one facilities=a+b+c=23+19+17=59

Hence, the probability that a person selected at random uses exactly one the facilities

$= \frac{59}{130}$