"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 other 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 take the switch?"(Assuming, of course, that you are after the car, not the goat)?
This popular puzzler created a stir in 1991 when it appeared in the newspaper1
and received a lot of wrong answers from readers, even from some who were mathematicians. How do we think about a problem like this, aÂ¬nd why is it so tricky?1Tierney, John
"Behind Monty Hall's Doors: Puzzle, Debate, and Answer?," New York Times, July 21, 1991.http://www.nytimes.com/1991/07/21/us/behind-monty-hall-s-doors-puzzle-debate-and-answer.html?pagewanted=all&src=pm
Further readingIsaac, R. The Pleasures of Probability
, Undergraduate texts in Mathematics, Springer, 1995.