Explanation Given Information: When Billy applied to Gigantic State U, 75% of all applicants were from the United States and 22% of those applicants were admitted. 14% of the foreign applicants were admitted. Formula used: Bayes’ theorem for two events: For two events A and T, Bayes’ theorem is defined as, P ( A | T ) = P ( T | A ) P ( A ) P ( T | A ) P ( A ) + P ( T | A ′ ) P ( A ′ ) Calculation: Consider the event that an application got admitted to be A and the event that the applicant was from the United States to be U . 75% of all applicants were from the United States. Thus, the probability that an applicant was from the United States is P ( U ) = 75 100 = 0.75 22% of the applicants from the United States were admitted. This can be rewritten as the percentage of applicant who were admitted, given that the applicant was from the United States. Thus, P ( A | U ) = 22 100 = 0.22 Since, the events that an applicant was from the United States and the applicant was not from the Unites States represent complementary events, that is, only one may occur, thus, P ( A ′ ) = 1 − P ( A ) = 1 − 0.75 = 0.25 There are 14% of the foreign applicants were admitted. This can be rewritten as the percentage of admitted, given that they were foreign. Thus, P ( A | U ′ ) = 14 100 = 0

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 8, Problem 54RE

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Chapter 8, Problem 53RE

Chapter 8, Problem 55RE

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Chapter 8 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 2E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 4E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 6E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 8E Ch. 8.1 - In Exercises 118, describe the sample space S of...Ch. 8.1 - Prob. 10E

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The percentage of admitted applicants was from the United States.

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