What's the probability that the other side of the coin is gold? 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.

50%. GIVEN that the first side you see is gold, what is the chance that you have the double-gold coin?
Assume you do this experiment a hundred times. In 50% of the cases you pull out a coin and see a gold side; the other 50% you see a silver side. In the latter case we have to discard the experiment and only count the cases where we see gold.
There is initially a 25% chance of double-gold, 25% chance double-silver, and 50% chance half-and-half. We discard the 25 cases where you draw the double-silver, and the 25 cases where you draw a half-and-half silver-side up. So of the 50 cases remaining, half are double-gold and half are gold-up silver-down.
Hence given that you have drawn a coin and see gold on top, there is a 50% there is gold on the bottom.  
