The Monty Hall problem is a classic brain teaser based on a television quiz show.
The puzzle involves three doors; behind one of them is a car. The other two doors conceal goats.
The aim of the puzzle is to maximize your chances of selecting the door leading to the car.
- You select one of three doors, which remains closed for now.
- The quiz host opens one of the other two doors, revealing a goat.
- You are now given the choice to switch your selection to the other closed door.
- PROBLEM: Statistically, should you stay or switch; or does it even matter?
Contrary to what most people logically expect, you are more likely to reveal the car if you switch.
Most people initally believe that the choice does not matter. Since there are two doors left, one would expect the odds of the car being behind any of the two doors to be 50/50.
In fact, switching your choice to the other door gives you a 2/3 chance to select the car, effectively doubling your odds.
A good way to understand the solution is to consider the two original unchosen doors as one single choice. The first choice results in one of the other possibilities being outed as revealing a goat. Thus the player effectively has the opportunity to choose the entire contents of two doors, if one switches from the first choice. This is illustrated below.