Explanation Given: In the population of 100 persons, 6 men have color-blindness and 1 woman have color blindness. Formula used: Conditional probability: Let A and B be two events then the conditional probability is given by, P ( A | B ) = P ( A ∩ B ) P ( B ) or P ( B | A ) = P ( A ∩ B ) P ( A ) The product rule based on conditional probability is, P ( A ∩ B ) = P ( A | B ) P ( B ) or P ( A ∩ B ) = P ( B | A ) P ( A ) Theorem used: Bayes’ Formula: Let U 1 , U 2 , ... , U n be n mutually exclusive events whose union is the sample space S . Let E be an arbitrary event in S such that P ( E ) ≠ 0 . Then, P ( U 1 | E ) = P ( U 1 ∩ E ) P ( E ) = P ( U 1 ∩ E ) P ( U 1 ∩ E ) + P ( U 2 ∩ E ) + ... + P ( U n ∩ E ) = P ( E | U 1 ) P ( U 1 ) P ( E | U 1 ) P ( U 1 ) + P ( E | U 2 ) P ( U 2 ) + ... + P ( E | U n ) P ( U n ) Similar results hold for U 2 , U 3 , ... , U n . Calculation: Define the events M as the person is man, W as person is woman, C as person has color-blindness, C ′ as person does not have color-blindness The probability of event M is, P ( M ) = 0

College Mathematics for Business, Economics, Life... (Instructor's)

14th Edition

ISBN: 9780134676104

Author: Barnett

Publisher: PEARSON

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Chapter 8, Problem 75RE

To determine

The probability that person is man, if a person is selected at random and is found to be

color-blind

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Chapter 8, Problem 74RE

Chapter 8, Problem 76RE

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Chapter 8 Solutions

College Mathematics for Business, Economics, Life... (Instructor's)

Ch. 8.1 - Repeat Example 1 for The outcome is a number...Ch. 8.1 - Prob. 2MP Ch. 8.1 - Prob. 3MP Ch. 8.1 - Suppose in Example 4 that after flipping the...Ch. 8.1 - Prob. 5MP Ch. 8.1 - Prob. 6MP Ch. 8.1 - Prob. 7MP Ch. 8.1 - Prob. 8MP Ch. 8.1 - Prob. 1ED Ch. 8.1 - Prob. 1E

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The probability that person is man, if a person is selected at random and is found to be color-blind