The Monty Hall Problem: There are three doors on the stage
clearly marked 1, 2, and 3. You as the player in this game are told that behind each of two doors there is a goat, and behind the other is a luxury car. The car is equally likely to be behind each door and its location is known to the game show host.
The rules of the game:
1. The player picks and announces a door number.
2. The host opens one of the other two doors to reveal a goat. 3. The player must decide whether or not to switch from the original choice to the other unopened door.
4. The player wins the object behind the final door choice.
The question: there are three doors, with a car behind one of them and two goats behind the other two doors. You select one door, and the host shows you which of the other two doors definitely does not contain the prize.
The task: stick with your choice, or do you change your mind to
choose another door.
The "Monty Hall Problem" is a classic example of the non-intuitive nature of probability
Possible arrangements:There shows the three possible
arrangements of one car and two goats behind three doors and the result of staying or switching after initially picking door 1 in each case:
behind behind behind result if staying at result if switching to the
door 1 door 2 door 3 door #1 door offered
Car Goat Goat Car Goat
Goat Car Goat Goat Car
Goat Goat Car Goat Car
Conclusion:A player who stays with the initial choice wins in only one out of three of these equally likely possibilities, while a player who switches wins in two out of three. The probability of winning by staying with the initial choice is therefore 1/3, while the probability of winning by switching is 2/3.