Ch. 5 - Discrete Probability Distributions

Triola - Elementary Statistics 14th Edition

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Triola 14th Edition

Ch. 5 - Discrete Probability Distributions

Problem 5.c.3d

Chapter 5, Problem 5.c.3d

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.

Verified step by step guidance

Step 1: Understand the problem. We are tasked with finding the probability that a randomly selected challenge was made by a man or was upheld with an overturned call. This involves using the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).

Step 2: Define the events. Let Event A be 'challenge made by a man' and Event B be 'challenge upheld with an overturned call'. From the table, we know the total number of challenges made by men is 160 + 398 = 558, and the total number of challenges upheld with overturned calls is 160 + 95 = 255.

Step 3: Calculate P(A). The probability of a challenge being made by a man is the number of challenges made by men divided by the total number of challenges: P(A) = 558 / 945.

Step 4: Calculate P(B). The probability of a challenge being upheld with an overturned call is the number of challenges upheld with overturned calls divided by the total number of challenges: P(B) = 255 / 945.

Step 5: Calculate P(A and B). The probability of a challenge being made by a man and upheld with an overturned call is the number of challenges that satisfy both conditions (160) divided by the total number of challenges: P(A and B) = 160 / 945. Finally, substitute these values into the formula P(A or B) = P(A) + P(B) - P(A and B) to find the desired 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 involves calculating the chance of selecting a challenge made by a man or one that was upheld with an overturned call from the total number of challenges. Understanding how to compute probabilities is essential for answering the question accurately.

Conditional Probability

Conditional probability refers to the probability of an event occurring given that another event has already occurred. In this scenario, it may be necessary to consider the relationship between challenges made by men and the outcomes of those challenges to determine the overall probability of interest. This concept helps in understanding how different events can influence each other.

Joint Probability

Joint probability is the probability of two events happening at the same time. In this case, it involves calculating the probability that a challenge was made by a man and that it resulted in an overturned call. This concept is crucial for combining probabilities of different events to find the overall likelihood of complex outcomes.

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Related Practice

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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.

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.

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Textbook Question

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Textbook Question

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