Suppose you have a cloth bag with one marble inside-either black or white, you don't know which. You add a white marble, shake the bag, and take out a marble at random. It's white. What are the odds that the remaining marble is white?
Hint: No...not ½.
(From The Universe in a Handkercheif, Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays, by Martin Gardner)