2SweetforTurtle posted...2/3 makes no sense. It says you picked from the same box, and already have a gold from the first pick. Therefore it CANNOT be the third box.
It does make sense. There are a total of 3 gold balls. If you take 1 golden ball from a random box, the odds that you took it from the box with 2 gold balls is 2/3, while the odds of taking it from the one with just 1 gold ball is 1/3. Thus, once you take 1 golden ball you know that there is a 2/3 chance that it's from the box with 2 golds.