I dagree with mr. whitte

the answer is 1/2

your can exclude pancake with two golden sides (g/g)

now i will use different notation for the pancakes: b/b is the pancake with two sides brown

you are either seeing the b side of the b/g pancake
or one of the b sides of a b/b pancake

however the b sides are identical (they are just described as brown)
picking up the b/b pancake either side up is still picking the same pancake
so in reality there are 2 pancakes you can choose

one of them gives the wanted result

therefore the answer is 1/2