There are 3 coins in a bag. One is a normal coin with "heads" on one side and "tails" on the other. The second one has "heads" on both sides and the third has "tails" on both sides.

Randomly draw one coin from the bag and put it on the table without looking at the down face.

The up face is a “heads”.

What is the probability the down face is “tails”?

Please justify your answer.

The answer is 1/3.

Lets assume each of the six faces has a mint mark and that all the marks are different. WLOG, assume the two-head coin has marks A and B on its two faces, the normal coin has C on its head side and D on its tail side, and the two-tailed coin has E and F on its faces.

Now, look at the face. It is heads so it can only have mark A, B or C on it. D, E, and F cannot appear since they are on tails faces. Of marks A, B, and C, two of the three marks belong to the two-head coin, whose bottom side is also heads. The remaining one of the three marks belong to the normal coin, whose bottom is tails, thus the probability is 1/3.