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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First, calculate the chance that the marble picked is white which is basically the chance of picking Bag X and picking a white ball from it + the chance of picking Bag Y and picking a white ball from it=
1/2 (5/9) + 1/2 (7/12)=5/18+7/24=41/72
Given that the marble is white, what is the probability it came from Bag X=> Since the event already occured, that the marble is white, we want to know the chance that the marble came from Bag X is = (5/18)/(41/72)= 20/41