I'd like to post my own (well, plagarised from here) problem to readers:
Without looking, you take out one chip, and lay it on the table.
1. Suppose the up-side turns out to be BLUE? What is the chance that the down-side will also be BLUE?
2. What if the up-side is RED? What is the chance that the down-side will also be RED?
3. Before you see how the chip has fallen, what is the chance that it has the same color dot on both sides?
4. Suppose you answered 1/2 in response to Questions 1 & 2. That would mean that whichever the up color of the chip, the chance is 50/50 that the color on the down side is the same. But if at Question 3 you said that chance is 2/3, aren't you contradicting yourself?
UPDATE: The original link to this problems source no longer appears to be active. You can try this one instead.