The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. Theconditional probabilities of event B given events A1, A2 and A3 are P(B | A1)=0.50, P(B | A2)=0.40and P(P | A3)=0.30.a) Calculate P (BQ A1), P(BQ A2) and P(BQ A3).b) Use Bayes' theorem to calculate the posterior probability P(A2 | B).c)Use the tree method to employ Bayes' theorem to calculate P(A1 | B), P(A2 | B), andP(A3 | B)

Given that , P(A1) = 0.20P(A2) = 0.50P(A3) = 0.300.500.400.30

Answered: The prior probabilities of events A1,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The prior probabilities for events A1, A2, and A3 are P(A1) = 0.10, P(A2) = 0.60, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B|A1) = 0.50, P(B|A2) = 0.40, and Р(B Аз) 3D 0.20. Round your answers to two decimal places. a. Compute P(B n A1) , P(BN A2), and P(BN A3). P(BN A1) = 0.05 P(BN A2) = 0.24 P(BN A3) = 0.06 b. Apply Bayes' theorem, to compute the posterior probability P(A2|B). P(A; N B ) = P(A;)P(B|A;) P(A1)P(B|A1 )+ P(A2)P(B|A2 )+...+ P(A,)P(B|A,) c. Use the tabular approach to applying Bayes' theorem to compute P(A1|B), P(A2|B), and P(A3|B). P(A; N B) Events P(A;) P(B|A;) P(A;|B) A1 A2 A3 Total:
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