The Monty Hall problem is a famous problem in probability (chance). The problem is based on a television game show from the United States, Let's Make a Deal. It is named for the host of this show, Monty Hall.

In the problem, there are three doors. A car (prize of high value) is behind one door and goats (booby prizes of low value) behind the other two doors. First, the player chooses a door but does not open it. Then the host, who has knowledge of what is behind every door, opens a different door which they are certain has a goat behind it (opening either door with equal chances if the car is behind the player's door). Last, the host lets the player choose whether to keep what is behind the first door or to change choices to the third door (the one the host did not open). The rules of the problem are that the host has to open a door with a goat behind and has to let the player switch. The question is whether changing choices increases the chances of getting the car.