Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. Y,, Y2, Y3 form a partition of S. P(X | Y,) = 0.3, P(X | Y,) = 0.4, P(X | Y3) = 0.5, P(Y,) = 0.4, P(Y,) = 0.1. Find P(Y, | X). P(Y, | X) =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places.

\(Y_1, Y_2, Y_3\) form a partition of \(S\). \(P(X \mid Y_1) = 0.3\), \(P(X \mid Y_2) = 0.4\), \(P(X \mid Y_3) = 0.5\), \(P(Y_1) = 0.4\), \(P(Y_2) = 0.1\). Find \(P(Y_1 \mid X)\).

\[P(Y_1 \mid X) =\] [textbox]
Transcribed Image Text:Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round your answer to four decimal places. \(Y_1, Y_2, Y_3\) form a partition of \(S\). \(P(X \mid Y_1) = 0.3\), \(P(X \mid Y_2) = 0.4\), \(P(X \mid Y_3) = 0.5\), \(P(Y_1) = 0.4\), \(P(Y_2) = 0.1\). Find \(P(Y_1 \mid X)\). \[P(Y_1 \mid X) =\] [textbox]
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