SWITCH to the other curtain!
Your initial probability of selecting the car was 1 in 3.
This means that your initial probability of NOT selecting the
car was 2 out of 3.
In other words, there was a 66.66% chance that you initially selected
a GOAT.
This probability did NOT change, merely because Monty Hall revealed
one of the goats to you, by opening one of the curtains you did
not select. This is the key to the solution. Because there
was a 66.66% chance that your initial selection was WRONG, you
will be most likely to select the car, if you SWITCH to the other
curtain. In switching to the other curtain, you will, in fact,
select the car 2 out of 3 times, or 66.66% of the time.
Random trials, using 3 index cards, will confirm this result, if you simulate a sufficient number of trials (20 - 50). As with any statistical probability, the MORE trials you do, the closer the result will be to the theoretically correct mathematical one; in this case selecting the car 66.66% of the time by SWITCHING, rather than retaining your initial selection.
Note to gamblers: This has implications for gambling in a casino. All games have an exact statistical probability (always in favor of the casino). The longer you sit and play, the closer will be the precise statistical result (you losing). Because of natural error occurring within a FEW trials, you increase your odds of winning if you place everything you are willing to bet on 1 or 2 games.
Monty Hall Problem websites:
Monty
Hall
Monty
Hall Simulation (java)
The
Let's Make a Deal Applet (Monty Hall Problem)
Monty
Hall Simulation
Monty Hall
Dilemma (simulation)
The Infamous
Monty Hall Problem
sci.math.faq
on the Monty Hall Problem
Monty
Hall Problem
Monty
Hall Problem; Bayes' Theorem
Three
Door Puzzle (Monty Hall Problem)
Quiz:
Win a Car (Monty Hall Problem)
The
Monte Hall Problem
Three
Door Puzzle: N-Doors (Monty Hall Problem)
Other References:
Steve Selvin, "A Problem in Probability", American Statistician 29:1 (Feb 1975), p. 67
Leonard Gillman, "The Car and the Goats", AMM 99:1 (Jan 1992), p. 3
Ed Barbeau, "The Problem of the Car and Goats", CMJ 24:2 (Mar 1993), p. 149