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.c.3e

Chapter 5, Problem 5.c.3e

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.

Verified step by step guidance

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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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 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.

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Related Practice

Textbook Question

In Exercises 25–28, find the probabilities and answer the questions.

Too Young to Tat Based on a Harris poll, among adults who regret getting tattoos, 20% say that they were too young when they got their tattoos. Assume that five adults who regret getting tattoos are randomly selected, and find the indicated probability.

c. Find the probability that the number of selected adults saying they were too young is 0 or 1.

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Textbook Question

Happiness In a survey sponsored by Coca-Cola, subjects were asked what contributes most to their happiness, and the table summarizes their responses. Does the table represent a probability distribution? Explain.

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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.

d. If 1 of the 945 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.

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Textbook Question

In Exercises 31 and 32, assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.75 probability that a pea has green pods (as in one of Mendel’s famous experiments).

Hybrids Assume that offspring peas are randomly selected in groups of 16.

c. Is a result of 7 peas with green pods a result that is significantly low? Why or why not?

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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

e. Find the standard deviation.

f. Find the variance.

Textbook Question

Salary Negotiations In a Jobvite survey, 2287 adult workers were randomly selected and asked about salary negotiations.

a. 29% of the respondents reported that they negotiated salary at their latest job. What is the number of respondents who reported that they negotiated salary?

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