A local country club has a membership of 600 and operates facilities that include an 18-hole championship golfcourse and 12 tennis courts. Before deciding whether to accept new members, the club president would like toknow how many members regularly use each facility. A survey of the membership indicates that 68% regularlyuse the golf course, 47% regularly use the tennis courts, and 6% use neither of these facilities regularly. Giventhat a randomly selected member uses the tennis courts regularly, find the probability that they also use thegolf course regularly.
A) 0.447
B) 0.309
C) 0.183
D) 0.223

Question

Quizplus · Accepted Answer

0.447Given that 68% of the members regularly use the golf course and 47% regularly use the tennis courts, with 6% not using either, we can deduce that 94% (100% - 6%) use at least one of the facilities. To find the probability that a member who uses the tennis courts also uses the golf course, we need to calculate the intersection of the two groups (those who use both facilities) and divide it by the percentage of members who use the tennis courts.Let's denote:- G as the event of regularly using the golf course,- T as the event of regularly using the tennis courts,- Neither as the event of not using either facility regularly.From the information given:- P(G) = 68%,- P(T) = 47%,- P(Neither) = 6%.We know that P(G or T) = P(G) + P(T) - P(G and T), and since 94% use at least one of the facilities (100% - 6%), we have:94% = 68% + 47% - P(G and T).Solving for P(G and T), we find:P(G and T) = 68% + 47% - 94% = 21%.The probability that a randomly selected member who uses the tennis courts also uses the golf course is the probability of the intersection of G and T (members who use both facilities) divided by the probability of T (members who use the tennis courts):P(G|T) = P(G and T) / P(T) = 21% / 47% ≈ 0.447.Therefore, the correct answer is A, 0.447.

A Local Country Club Has a Membership of 600 and Operates