Y1 Y2 Y3 form a partition of S PXY1 1 PXY2 3 PXY3 6 PY1

Y₁, Y₂, Y₃ form a partition of S. P(X|Y₁) = .1, P(X|Y₂) = .3, P(X|Y₃) = .6, P(Y₁) = .4, P(Y₂) = .2. Use Bayes\' theorem or a tree diagram to calculate P(Y₁|X). (Round your answers to four decimal places.)

P(Y1/0+P(Y2)+P(Y3)=1
=>P(Y3)=1-(0.2+0.4)=0.4
USING BAYES THEROM
P(Y1/X)=P(X/Y1)*P(Y1)/(P(X/Y1)*P(Y1)+P(X/Y2)*P(Y2)+P(X/Y3)*P(Y3)
SUBSTITUTING THE VALUES
=>P(Y1/X)=0.1176

$Y1, Y2, Y3 form a partition of S. P(X|Y1) = .1, P(X|Y2) = .3, P(X|Y3) = .6, P(Y1) = .4, P(Y2) = .2. Use Bayes\' theorem or a tree diagram to calculate P(Y1|X).$

Y1 Y2 Y3 form a partition of S PXY1 1 PXY2 3 PXY3 6 PY1

Solution

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