Bags of Marbles Puzzle

The Puzzle:

Bags of Marbles
You have three bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white marble and one black marble.

You pick a random bag and take out one marble.

It is a white marble.

What is the probability that the remaining marble from the same bag is also white?
Do you have the answer? Check against our solution!