Question

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members, the club president would like to know how many members use each facility. A survey of the membership indicates that 75% use the golf course, 50% use the tennis courts, and 5% use neither of these facilities. One club member is chosen at random. What is the probability that the member uses the golf course but not the tennis courts

Answer 1

0.45 = 45% probability that the member uses the golf course but not the tennis courts

Explanation:

I am going to solve this question using the events as Venn sets.

I am going to say that:

Event A: Uses the golf courses.

Event B: Uses the tennis courts.

5% use neither of these facilities.

This means that
`P(A \cup B) = 1 - 0.05 = 0.95`

75% use the golf course, 50% use the tennis courts

This means, respectively, by:

`P(A) = 0.75, P(B) = 0.5`

Probability that a member uses both:

This is
`P(A \cap B)`. We have that:

`P(A \cap B) = P(A) + P(B) - P(A \cup B)`

So

`P(A \cap B) = 0.75 + 0.5 - 0.95 = 0.3`

What is the probability that the member uses the golf course but not the tennis courts?

This is
`P(A - B)`, which is given by:

`P(A - B) = P(A) - P(A \cap B)`

So

`P(A - B) = 0.75 - 0.3 = 0.45`

0.45 = 45% probability that the member uses the golf course but not the tennis courts