A local country club has a membership of 600 and operates facilities that includ

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?

Explanation / Answer

Ans:

P(golf course)=0.75

P(tennis)=0.5

P(neither golf course nor tennis)=0.05

P(golf course or tennis)=1-P(neither golf course nor tennis)=1-0.05=0.95

Now,

P(golf course or tennis)=P(golf course)+P(tennis)-P(golf course and tennis)

0.95=0.75+0.5-P(golf course and tennis)

P(golf course and tennis)=0.75+0.5-0.95=0.3

So,

P(golf course but not tennis)=P(golf course)-P(golf course and tennis)

=0.75-0.3

=0.45

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