A bag contains one stone of unknown color, either black or white. A white stone is added to the bag.

The bag is shaken and a stone is removed without looking; it turns out to be a white one.

What are the chances of the remaining stone being white?

*(Hint: The answer is NOT 1 in 2.)*

### Solution to the Two Stones Puzzle

The odds of the remaining stone being white are not 1 out of 2 because there are 3 possible outcomes, not just 2. As it turns out, the chances are 2 out of 3.

Here are the three possibilities:

- The original stone was black. If a white stone is added and a white stone removed, the remaining stone must be the black one.
- The original stone was white, and the white stone that gets removed is the original one. What's left, then, is the white stone that was added.
- The original stone was white, and the white stone that gets removed is the added one. What's left, then, is the original white stone.

The above 3 possibilities are the only possibilities there are, and they're all equally likely. In the first case, the remaining stone is black; in the second and third cases, the remaining stone is white. That is, the remaining stone is white in 2 out of 3 of the equally likely possibilities.

The reason the chances are not the expected 1 out of 2 is the specification that a white stone was drawn from the bag. This was a forced result, not a random result, and thereby affected the odds of the remaining stone being white.