Has everyone heard of the Game Show problem? It is also known as the Monte Hall problem [wikipedia.org]. This is a notoriously deceptive problem in probability that usually sparks fierce debate anytime it is brought up. It was once described in Marilyn vos Savant's Ask Marilyn column in Parade magazine as the following:
"Suppose 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 No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to switch your choice?"Most people will conclude that there is a 50/50 chance of winning if you switch, but the actual answer is far more interesting.
I made the mistake of posing this problem to my college-aged nephews over the holidays, and now Heimlich wants to kill me because of the length of the ensuing debate.
The solution is counter-intuitive and most people won't believe it until a demonstration is given. We used cards to represent the three doors, and my nephews were astounded to find that they won almost every time if they chose to switch.
If you are interested in a thought-provoking puzzle and haven't heard of this one before, I urge you to read the solution (one explanation can be found on the Wikipedia article linked to above).
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