You are on a gameshow. The gameshow host tells you there are three doors. Behind two of the doors are a goat and behind one of the doors is a million dollars.
He tells you he will reveal a different door after you make you selection.
You pick one door and he then opens a different door to reveal a goat. He then offers you the option to switch doors. Should you change the door you picked? Keep it. Or does it not matter?
Go over the chances of picking a million dollars from each door.
You should switch doors.
The chance of you picking correctly initially was 1/3.
The 2/3 times you picked incorrectly, by changing doors you get a 100% of getting the million dollars. Because there is only one door left.
Therefore the chance initially was 1/3 and by switching you have 2/3 of getting the million dollars