Are you familiar with The Monty Hall Problem? It's sometimes called The Monty Hall Paradox.
Here's how it works. You're on a game show not unlike Mr. Hall's legendary Let's Make a Deal. There are three doors. One of them conceals a new car. The other two have goats behind them. You get to pick a door and you will win the prize behind it. Obviously, the idea is to go home with a car, not a goat.
So you pick your door. Then the host (who knows where the car is hidden) says, "Let's see what's behind one of the doors you didn't pick!" He opens one of the doors that conceals a goat. You feel lucky you did not pick that door.
The host then asks you, "Before we reveal the prize behind the door you selected, would you like to swap? Would you like to take the other door instead of the one you picked?"
The problem: Should you swap? Would it make you more likely to win the car, less likely…or would it make no difference?
Most people say it would make no difference. Amazingly, they are wrong. You double the odds of winning the car if you switch.
Just why this is so is hard to explain. There are dozens of videos on the 'net in which folks attempt to explain why one should always switch and most of them are incomprehensible and confusing. The one below is the best one I've come across.
If you'd like to see an interesting test of this situation, this webpage allows everyone to play the game and it tallies up the results. As you'll see, those who choose to swap win twice as often as those who don't. I know it's counter-intuitive but if you think about it, it makes sense.