Marble Garble (Hint: It's not obvious)

You have 3 bags, each containing 2 marbles. Bag A contains 2 white marbles, Bag B contains 2 black marbles, and Bag C contains 1 white marble and 1 black marble.You pick a random bag and it is a white marble. What is the probability that the remaining marble from the same bag is also white?

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