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 regularly use each facility. A survey of the membership indicates that 61% regularly use the golf course, 45% regularly use the tennis courts, and 3% use neither of these facilities regularly. What percentage of the 600 uses at least one of the golf or tennis facilities?

• A. 97%
• B. 3%
• C. 103%
• D. 9%

Hint:

"At least one" is the complement of "neither"; use \(P(G\cup T)=1-P(\text{neither})\).

Answer 1

The Correct Option is A

Step 1: Convert the percentages into member counts out of 600. Members using neither facility: $0.03 \times 600 = 18$ members.
Step 2: The members using at least one of golf or tennis are all the members except those 18 who use neither:\[ \text{Members using at least one} = 600 - 18 = 582 \]
Step 3: Express this as a percentage of the total membership:\[ \frac{582}{600} \times 100\% = 97\% \]
Step 4: This confirms, without needing the individual golf (61%) and tennis (45%) figures directly, that "at least one" usage is exactly the complement of "neither".\[\boxed{97\%}\]