Tennis Challenge In a recent U.S. Open tennis tournament, there were 945 challenges made by singles players, and 255 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.

e. If one of the challenges is randomly selected, find the probability that it was made by a man, given that the challenge was upheld with an overturned call.

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the probability that a challenge was made by a man, given that the challenge was upheld with an overturned call. This is a conditional probability problem, and we will use the formula for conditional probability: P(A|B) = P(A and B) / P(B).

Step 2: Identify the relevant data from the table. The number of challenges upheld with overturned calls by men is 160, and the total number of challenges upheld with overturned calls (both men and women) is 160 + 95 = 255.

Step 3: Calculate P(B), the probability that a challenge was upheld with an overturned call. This is the total number of challenges upheld with overturned calls divided by the total number of challenges made, which is 255 / 945.

Step 4: Calculate P(A and B), the probability that a challenge was made by a man and upheld with an overturned call. This is the number of challenges upheld with overturned calls by men divided by the total number of challenges made, which is 160 / 945.

Step 5: Use the conditional probability formula to find P(A|B). Divide P(A and B) by P(B). This gives (160 / 945) / (255 / 945). Simplify the expression to find the probability.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it helps determine the chance of selecting a challenge made by a man, given that the challenge was upheld with an overturned call. Understanding how to calculate conditional probability is essential for solving the question.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), meaning the probability of event A occurring given event B. In this scenario, we need to find the probability of a challenge being made by a man (event A) given that it was upheld with an overturned call (event B).

Data Interpretation

Data interpretation involves analyzing and making sense of data presented in various forms, such as tables or graphs. In this case, the table provides the number of challenges upheld and rejected by gender, which is crucial for calculating the required probabilities. Being able to extract relevant information from the data is key to answering the question accurately.