TITLE: What's the probability that the other side of the coin is gold?
QUESTION [6 upvotes]: 4 coins are in a bucket: 1 is gold on both sides, 1 is silver on both sides, and 2 are gold on one side and silver on the other side.
I randomly grab a coin from the bucket and see that the side facing me is gold. What is the probability that the other side of the coin is gold?
I had thought that the probability is $\frac{1}{3}$ because there are 3 coins with at least one side of gold, and only 1 of these 3 coins can be gold on the other side. However, I suspect that the sides might be unique, which derails my previous logic.

REPLY [3 votes]: I randomly grab a coin from the bucket and see that the side facing me is gold.

As any good brain-teaser, it distracts you from the fact that, for all purposes, you randomly selected a coin side that happened to be golden (4 total), not a coin with at least one goden side (3 total). There is 2/4 chance of having selected a coin with both sides golden, and 1/4 chance each for the G/S coins - meaning that there's a total 1/2 chance flipping the coin would reveal the other side is golden as well.
This is a variation of Bertrand's box paradox.