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?

This is a classic conditional probability problem. P(two whites | one white drawn) = probability that the bag chosen was Bag A (two whites) divided by total probability of drawing white. P(Bag A | white) = (1 × 1/3) / [(1 × 1/3) + (0.5 × 1/3) + (0 × 1/3)] = (1/3) / (1/2) = 2/3. Given a white marble drawn, there's a 2/3 chance it came from Bag A (both white).