Puzzles/Statistical puzzles/3 Bags of Marbles

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Puzzles | Statistical puzzles | 3 Bags of Marbles

You have three bags, each containing two marbles. Bag #1 contains two white marbles, bag #2 contains two black marbles, and bag #3 contains one white marble and one black marble.

You pick a random bag and take out one marble. Given that this is a white marble, what is the probability that the remaining marble from the same bag is also white?