Compute Conditional Probabilities
-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 $62 \%$ regularly use the golf course, $43 \%$ regularly use the tennis courts, and $4 \%$ use neither of these facilities regularly. Given that a randomly selected member uses the tennis courts regularly, find the probability that they also use the golf course regularly.
A) $0.209$
B) $0.145$
C) $0.086$
D) $0.094$

Question

Quizplus · Accepted Answer

Given that a member uses the tennis courts regularly, the probability they also use the golf course regularly can be found using the formula for conditional probability. First, calculate the percentage of members who use both facilities. Since $62\% + 43\% - 4\% = 101\%$, and the total cannot exceed $100\%$, the overlap (those who use both facilities) is $101\% - 100\% = 1\%$. However, this calculation is incorrect due to a misunderstanding of the problem setup. The correct approach is to recognize that $96\%$ of members use at least one of the facilities (since $4\%$ use neither), and the overlap must be calculated differently.The correct calculation involves understanding that the $4\%$ who use neither facility are not directly relevant to finding the overlap. Instead, we should focus on the fact that $43\%$ use the tennis courts. To find the percentage of tennis court users who also use the golf course, we need to calculate the overlap based on the given percentages.The correct approach is to use the information given to directly calculate the probability of a member using the golf course given they use the tennis courts. This involves understanding the relationship between the percentages of users for each facility and the total membership.Given the error in the initial explanation and calculation, the correct answer should be recalculated based on the correct interpretation of the problem statement. The initial calculation mistakenly subtracted the $4\%$, leading to an incorrect approach. The correct method involves directly calculating the conditional probability based on the given percentages and the total membership, without incorrectly subtracting the $4\%$.To correctly calculate the conditional probability:- We know $62\%$ of members use the golf course, and $43\%$ use the tennis courts.- The question asks for the probability that a member uses the golf course given they use the tennis courts.The correct calculation should consider the proportion of members who use both facilities out of those who use the tennis courts. However, without the exact number of members who use both, we cannot directly calculate this probability from the information given. The initial approach to subtract $4\%$ was incorrect because it misunderstood the problem's requirements.Given the misunderstanding in the explanation, the correct answer would involve re-evaluating the information provided to accurately calculate the conditional probability based on the correct interpretation of the given percentages and the total membership. The calculation of the overlap and the conditional probability requires correct application of the principles of conditional probability, which was not accurately applied in the initial explanation.

Compute Conditional Probabilities -A Local Country Club Has a Membership 62%62 \%62%

Compute Conditional Probabilities
-A Local Country Club Has a Membership $62 \%$