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

question 94

Short Answer

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places.
​ $Y _ { 1 }$ , $Y _ { 2 }$ , $Y _ { 3 }$ form a partition of S.
​ $P \left( X \mid Y _ { 1 } \right) = 0.4$ , $P \left( X \mid Y _ { 2 } \right) = 0.5$ , $P \left( X \mid Y _ { 3 } \right) = 0.6$ , $P \left( Y _ { 1 } \right) = 0.8$ , $P \left( Y _ { 2 } \right) = 0.1$ .
​
Find $P \left( Y _ { 1 } \mid X \right)$ .
​ $P \left( Y _ { 1 } \mid X \right) =$ __________