The "Monty Hall" puzzle
Problem statement
You’re on a game show, and you’re given the choice of three doors.
Behind one door is a car, behind the others, goats. You can choose
any door, and you'll receive what's behind it as a prize. You pick
a door, say #1, and the host, who knows what’s behind the doors,
opens another door, say #3, which has a goat. He says to you, "Do
you want to stick with door #1, or switch to door #2?" Is it to your
advantage to switch your choice of doors?
Solution to metapuzzle: show
Restated puzzle: show
You’re on a game show, and you’re given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to stick with #1 or switch to #2?" You knew he was going to do this, whichever door you had chosen. It's in his script, and he does it every week. Is it to your advantage to switch your choice of doors?
Solution to puzzle: show
If you stay with your original choice of door, your chance of winning continues to be ⅓. If you switch, it therefore becomes ⅔. You should switch.
Comments: show
The problem statement above (without the italics) is by Marilyn vos Savant. When she supplied the "correct", and intended, answer that you should switch, she received thousands of letters claiming that she was mistaken.
My view is that at least some of those who considered her answer mistaken had been led "astray" by the cynical consideration I give above. But it seems that many others were answering her intended question, and getting the answer wrong anyway.
I believe the intended puzzle (but not the metapuzzle) is a good one. It's a pity it is spoiled by being misstated in most sources.
Source: Steve Selvin, in The American Statistician Volume 29, 1975 - Issue 1.
Brought to public attention by Marilyn vos Savant in Parade, vol. 16, 1990-09-09
This is one of several pages on puzzles and metapuzzles.