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.





b. If one of the overturned calls is randomly selected, what is the probability that the challenge was made by a woman?

Verified step by step guidance

1. Step 1: Identify the relevant data from the table. The overturned calls are listed under 'Challenge Upheld with Overturned Call'. For men, there are 160 overturned calls, and for women, there are 95 overturned calls.
2. Step 2: Calculate the total number of overturned calls. Add the overturned calls for men and women: 160 + 95.
3. Step 3: Determine the probability formula. The probability of selecting an overturned call made by a woman is given by the ratio of overturned calls made by women to the total number of overturned calls.
4. Step 4: Write the probability formula using MathML: $\frac{95}{160+95}$
5. Step 5: Simplify the formula to find the probability. Divide the number of overturned calls made by women (95) by the total number of overturned calls (160 + 95).

Key Concepts

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 that a randomly selected overturned call was made by a woman. The formula for probability is the number of favorable outcomes divided by the total number of possible outcomes.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this scenario, we are interested in the probability of a challenge being made by a woman, given that it was one of the overturned calls. This concept is crucial for understanding how to refine probabilities based on specific conditions.

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 information on the number of challenges upheld and rejected by gender, which is essential for calculating the required probability. Understanding how to extract relevant information from data is key to solving statistical problems.