No relation to the sampling problem being discussed here but another question which cuts hard against common sense is the tile problem.
A bag contains three tiles. One tile has an "X" on both sides, one has an "0" on both sides, and the last one has an "X" on one side and an "0" on the other. If you draw one at random and hold it up where you can only see the side facing you on which there is an "X", what is the probability that there is also an "X" on the other side?
A bag contains three tiles. One tile has an "X" on both sides, one has an "0" on both sides, and the last one has an "X" on one side and an "0" on the other. If you draw one at random and hold it up where you can only see the side facing you on which there is an "X", what is the probability that there is also an "X" on the other side?