How do you do this (Bayes' Theorem)

Y1, Y2, Y3 form a partition of S. P(X|Y1) = .8, P(X|Y2) = .1, P(X|Y3) = .1, P(Y1) = .3, P(Y2) = .2. Use Bayes' theorem or a tree diagram to calculate P(Y1|X).

P(Y1 | X) = P(X Y1)/P(X)

What is P(X)? It's P(X|Y1) P(Y1) + P(X|Y2) P(Y2) + P(X|Y3) P(Y3).

What is P(X Y1)? Using P(X | Y1) = P(X Y1)/P(Y1), then P(X Y1) = P(X | Y1) P(Y1)

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