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The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. The conditional probabilities of event B given events A1, A2 and A3 are P(B | A1)=0.50, P(B | A2)=0.40 and 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), and P(A3 | B)

The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. The conditional probabilities of event B given events A1, A2 and A3 are P(B | A1)=0.50, P(B | A2)=0.40 and 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), and P(A3 | B)

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
Problem 84CR
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The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. The conditional probabilities of event B given events A1, A2 and A3 are P(B | A1)=0.50, P(B | A2)=0.40 and 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), and P(A3 | B)
Transcribed Image Text:The prior probabilities of events A1, A2 and A3 if P(A1)=0.20, P(A2)=0.50 and P(A3)=0.30. The conditional probabilities of event B given events A1, A2 and A3 are P(B | A1)=0.50, P(B | A2)=0.40 and 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), and P(A3 | B)
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