This problem is similar to the Monty Hall problem. In this case the pancake that is golden on both sides is a priori eliminated. Let's call the remaining pancakes P₁ and P₂. We use the letters G and B to indicate whether a side is golden versus brown. Upper and lower case letters are used to distinguish one side from the other. The table below lists all the possibilities, e.g. the first row would indicate a trial where P₁ was selected and it's golden side is on the top. Since we know that a brown side was on top, only the last three rows would apply and of these 2/3 are brown on the other side.