Ch. 5 - Discrete Probability Distributions

Triola - Elementary Statistics 14th Edition

Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook

Triola 14th Edition

Ch. 5 - Discrete Probability Distributions

Problem 5.CRE.3b

Chapter 5, Problem 5.CRE.3b

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

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.

Step 2: Calculate the total number of overturned calls. Add the overturned calls for men and women: 160 + 95.

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.

Step 4: Write the probability formula using MathML:

\frac{95}{160 + 95}

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).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

Planets The planets of the solar system have the numbers of moons listed below in order from the sun. (Pluto is not included because it was uninvited from the solar system party in 2006.) Include appropriate units whenever relevant.

0 0 1 2 17 28 21 8

c. Find the mode.

d. Find the range.

Textbook Question

Find the mean of the random variable x described in the preceding exercise.

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Textbook Question

Kentucky Pick 4 In the Kentucky Pick 4 lottery game, you can pay \$1 for a “straight” bet in which you select four digits with repetition allowed. If you buy only one ticket and win, your prize is \$2500.

c. If you play this game once every day, find the probability of no wins in 365 days.

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Textbook Question

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.

c. If two different challenges are randomly selected without replacement, find the probability that they both resulted in an overturned call.

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Textbook Question

a. If you buy one ticket, what is the probability of winning?

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Textbook Question

0 0 1 2 17 28 21 8

a. Find the mean.

b. Find the median.