Consider a game show, in which the game show host asks you to pick a prize behind one of three doors.
After he asks you to pick, the game show host doesn't open the door you picked. Instead, he opens a different door...one which he already knows is empty. Now, having eliminated one of the choices, he asks you, "Do you want to keep your guess? Or change it?"
Typically, people will answer, "There's a 1 in 2 chance that I'll get it right, so it doesn't make any difference if I change my guess or not, the probability is 1/2 either way!"
And the typical answer is not correct. Surprisingly, your odds are better if you change your guess. Why? Because the odds that you guessed incorrectly in the first place are 2 in 3, or 2/3. The game show's action of opening a door does not change that probability. Which means the odds are better if you switch doors. In fact, 2 times out of 3, you'll be better off switching.
This is called the Monty Hall Problem.