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 regularly use each facility. A survey of the membership indicates that 70% regularly use the golf course, 49% regularly use the tennis courts, and 10% use neither of these facilities regularly. Given that a randomly selected member uses the tenis courts regularly, find the probability that they also use the golf course regularly

0.322

0.414

0.244

0.592

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 70% regularly use the golf course, 49% regularly use the tennis courts, and 10% use neither of these facilities regularly. Given that a randomly selected member uses the tenis courts regularly, find the probability that they also use the golf course regularly

0.322

0.414

0.244

0.592

Explanation / Answer

P( Golf) = 0.70, P(Tennis) = 0.49, P( Golf OR tennis)c = 0.10

We have to find conditional probability P( Golf | tennis) = ?

P(Golf OR Tennis) = 1 - P( Golf OR Tennis)c  

= 1 - 0.10

= 0.90

[ Use formula P( A OR B) = P(A) + P(B) - P(A AND B) ]

P( Golf OR Tennis) = P(Golf) + P(Tennis) - P(Golf AND Tennis)

P(Golf AND Tennis) = P(Golf) + P(Tennis) - P( Golf OR Tennis)

= 0.70 + 0.49 - 0.90

= 0.29

So,

P( Golf | tennis) = P( Golf AND tennis) / P( Tennis)

= 0.29 / 0.49

= 0.592

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