>>12094599If they were all in the same box you would be right, but this is not the case. Rather, there are three equally likely gold balls to have been grabbed first. Any scenario where a grey ball would have been grabed first has been excluded and so is discarded. Once a ball has been chosen, all that matters is the other ball in the box.
Balls 1 and 2 are in a box with another gold ball, and so result in a win. Ball 3 is in a box with a grey ball, and so if chosen results in a loss. 2 of 3 equally likely scenarios result in a win, and so the odds are 2/3.
