The Monty Hall Problem by Darrin Chandler
The Problem
There are three doors. Behind one door is a new car. Behind the other two are goats. You are asked to pick a door. Then a different door is opened to reveal one of the goats. You are now asked if you would like to stay with your original door, or switch to the one remaining door.
Should you stay or switch? Does it make any difference?
The Answer
Switch! If you stay with your original door your chances are 1 in 3. If you switch your chances are 2 in 3!
Why?
When you first pick there are three available doors, and your changes are 1/3. Pretty much everyone grasps this immediately. When a losing door is revealed, you are given additional, relevant information that you did not originally have. This must affect the odds.
When you first pick, the odds of that door being the winner are 1/3. If you take no further action then the odds don't either. There is now only one remaining choice, but the sum of all choices still tally to 100%. The other door, therefore, has a 2/3 chance of being the winner.
References
Here's an informative write-up of Marilyn vos Savant's tribulations in publishing this puzzle.
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