Not as easy as it looks

I have two bags of marbles, Bag X and Bag Y. Bag X contains 4 black marbles and 5 white marbles. Bag Y contains 5 black marbles and 7 white marbles. I choose a bag at random, and then randomly choose a marble from the bag. The marble is white; what is the probability it came from Bag X?

Image Credit: Flickr R.Berdar
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