Bags of Marbles

You have three identical bags, each containing two marbles. Bag A contains two white marbles, Bag B contains two black marbles, and Bag C contains one white and one black marble. You pick a bag at random and draw out one marble. If the marble is white, what is the probability that the other marble in the same bag is also white? Click below to see the answer.

Many people will instinctively answer 50%, or 1/2, since the marble has two possible colors, but the probability is actually 2/3 (66.67%). Why? If the first marble is white, then you know you didn't randomly select Bag B. That means that the first marble you selected has three (not two) possibilities:

1. The first marble in Bag A.
2. The second marble in Bag A.
3. The white marble in Bag C.

Only in the third case will the other marble be black, so there's a 2/3 probability that when the first marble is white, the second marble will also be white.

If you want to see how you would model this problem in Python, you can look at my solution on GitHub.