The prior probabilities for events A₁, A2, and A3 are P(A₁) = 0.20, P(A₂) = 0.30, and P(A3) = 0.50. The conditional probabilities of event B given A₁, A₂, and A3 are P(B | A₁) = 0.50,P(B | A₂) = 0.30, and P(B | A3) = 0.40. (Assume that A₁, A₂, and A3 are mutually exclusive events whose union is the entire sample space.)(a) Compute P(B ŉ A₁), P(B n A₂), and P(B n A3).P(B n A₁)P(B n A₂)=P(B n A3)=P(A₁)P(B | A₁)(b) Apply Bayes' theorem, P(A¡ | B)=7to compute the posterior probability P(A₂ | B). (Round your answer to two decimalP(A₁)P(B | A₁) + P(A₂)P(B | A₂) ++ P(An)P(B | An)'places.)(c) Use the tabular approach to applying Bayes' theorem to compute P(A₁ | B), P(A₂ | B), and P(A3 | B). (Round your answers to two decimal places.)Events P(A₁) | P(B | A;)P(A¡n B)P(A¡ | B)A₁0.200.50A₂0.300.30A30.500.401.001.000.00

Answered: Image /qna-images/answer/cefc4ee2-c3ac-41de-b09c-a227cd77ae3c.jpg

Answered: The prior probabilities for 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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Q. 2 A car dealer notes the following probabilities about his customers: P(those who buy a new car) = 0.25 P(those who buy a European car) = 0.30 P(those who neither buy a new car nor an European car) = 0.54 Find the probability that next customer buys a new European car?
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