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Use Bayes' Theorem or a Tree Diagram to Calculate the Indicated

question 49

Multiple Choice

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places.
Y1Y _ { 1 } ,
Y2Y _ { 2 } , Y3Y _ { 3 } form a partition of S.
P(XY1) =0.4P \left( X \mid Y _ { 1 } \right) = 0.4 , P(XY2) =0.5P \left( X \mid Y _ { 2 } \right) = 0.5 , P(XY3) =0.7P \left( X \mid Y _ { 3 } \right) = 0.7 , P(Y1) =0.7P \left( Y _ { 1 } \right) = 0.7 , P(Y2) =0.1P \left( Y _ { 2 } \right) = 0.1 .

Find P(Y1X) P \left( Y _ { 1 } \mid X \right) .

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