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.

a. If 1 of the 945 challenges is randomly selected, what is the probability that it resulted in an overturned call?

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected challenge resulted in an overturned call. This is a probability problem where we use the formula for probability: P(Event) = (Number of favorable outcomes) / (Total number of outcomes).

Step 2: Identify the favorable outcomes. From the table, the number of challenges that resulted in an overturned call is the sum of 'Challenge Upheld with Overturned Call' for both men and women. Add 160 (men) and 95 (women) to get the total number of overturned calls.

Step 3: Identify the total number of outcomes. The total number of challenges made is given as 945 in the problem statement.

Step 4: Write the probability formula. Substitute the values into the formula: P(Overturned Call) = (Total number of overturned calls) / (Total number of challenges).

Step 5: Simplify the fraction to express the probability. Divide the total number of overturned calls by the total number of challenges to get the probability. Leave the result in fraction or decimal form as required.

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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 is used to determine the chance that a randomly selected challenge from the total number of challenges resulted in an overturned call. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Favorable Outcomes

Favorable outcomes refer to the specific results that align with the event of interest in a probability scenario. In this case, the favorable outcomes are the challenges that resulted in overturned calls, which total 255. Understanding how to identify and count these outcomes is crucial for calculating the probability accurately.

Total Outcomes

Total outcomes represent the complete set of possible results in a probability experiment. For this question, the total number of challenges made is 945. Knowing the total outcomes is essential for determining the probability, as it serves as the denominator in the probability formula, allowing for a comparison between favorable and total outcomes.