Monty Hall Problem
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The Monty Hall problem is a puzzle. It has to do with chance.
The puzzle is based on America's game show Let's Make a Deal. The name comes the show's host, Monty Hall.
You are on a game show. You can choose three doors.
Behind one door is a car. The other two doors have goats.
You choose a door, number one. The game host opens a door, number two, with a goat.
He asks, “Would you like to switch?”. Is it good to switch your choice?
When the host opens a door with a goat, there are two doors left. One of the doors has the car, the other has a goat.
Many people assume each door has an equal chance of having a car. They do not think changing your choice matters. This is wrong.
[edit] How it Works
The player has a 1/3 chance of choosing the car. They have a 2/3 chance of choosing a goat. In both cases the host reveals a goat.
If the player first chose the car, switching loses.
If the player chose a goat, the host shows the other goat. Switching will win the car.
Switching makes the chances of winning the car go from 1/3 to 2/3.
This may be easier to learn with more doors.
Think of 100 doors, one with a car and 99 with goats. You choose a door.
The game host opens 98 doors with goats. You are asked to switch.
The chance the player chooses the car is very small. The player has a 1/100 chance!
Switching in this case makes the chance better.
[edit] External links
- Monty Hall Problem at Wolfram MathWorld
- Graphical Proof of the Monty Hall Problem (tea cups and diamonds)
- A Monty Hall Simulator in Javascript (A Simulator that you can run in your web browser. )
- Realtime global simulation A simulation which tallies up the results from every user who has ever played.
- The Monty Hall Problem Web Page A simple presentation of the problem and its solution.
- A tree-diagram of the Monty Hall problem under the Marilyn vos Savant assumptions
- The Game Show Problem The original question and responses on Marilyn's web site.
