Bertrand's box paradox
There are three boxes, one with two gold coins, one with one gold and one silver, one with two silver. A coin drawn at random is gold. What is the probability that the other coin in the same box is gold? The coin came either from the first box, or the second; there is no reason for preferring either, so the chance should be a half. But the coin picked was either the first in the first box, or the second in the first box, or the one gold coin in the second box. Two of these three possibilities give it that the other coin in the same box is gold, so the probability is 2/3.