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

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

Step-by-step 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

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

This means, respectively, by:

Probability that a member uses both:

This is . We have that:

So

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

This is , which is given by:

So

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