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

Multiple Choice

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.
$P \left( X \mid Y _ { 1 } \right) = 0.4$ , $P \left( X \mid Y _ { 2 } \right) = 0.5$ , $P \left( X \mid Y _ { 3 } \right) = 0.7$ , $P \left( Y _ { 1 } \right) = 0.7$ , $P \left( Y _ { 2 } \right) = 0.1$ .

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

A) $P \left( Y _ { 1 } \mid X \right) = 0.1064$
B) $P \left( Y _ { 1 } \mid X \right) = 0.5957$
C) $P \left( Y _ { 1 } \mid X \right) = 0.2979$
D) $P \left( Y _ { 1 } \mid X \right) = 0.4043$
E) $P \left( Y _ { 1 } \mid X \right) = 0.098$