a. Explanation Given info: Here P ( A 1 ) = 0.5 , P ( A 2 ) = 0.2 , P ( A 3 ) = 0.3 , P ( B | A 1 ) = 0.4 , P ( B | A 2 ) = 0.8 and P ( B | A 3 ) = 0.6 Calculation: Rule of Total Probability The events A 1 , A 2 , ... , A K are mutually exclusive and exhaustive. Then the probability of any event B can be obtained as follows: P ( B ) = ∑ j = 1 k P ( A j ) . P ( B | A j ) Here P ( B ) = P ( B | A 1 ) P ( A 1 ) + P ( b. To determine To find: The probability of P ( A 1 | B ) using the Bayes rule.

10th Edition

ISBN: 9780321989178

Author: Neil A. Weiss

Publisher: PEARSON

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Chapter 4.7, Problem 213E

To determine

To find: The probability of P(B) using the rule of total probability.

To determine

To find: The probability of P(A1|B) using the Bayes rule.

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Chapter 4.7, Problem 212E

Chapter 4.7, Problem 214E

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The probability of P ( B ) using the rule of total probability.

Solution Summary: The author calculates the probability of P(B) using the rule of total probability.