The question as it appears in the 05/01 edition of Specs & Techs from GlobalSpec:
On a game show, a contestant is offered the choice of three doors. A goat is behind two of them, a new car behind the third. The contestant picks one door, but the host opens a different door showing a goat. With two doors left, the host again asks which door? To maximize the probability to win the car, should the contestant stay with the first guess, or switch to the other door? Explain the reason behind your answer.
Thanks to Blink who submitted the original question (which we revised a bit)
(Update: May 8, 2:04 AM) And the Answer is...
This puzzle is often called the Monty Hall Paradox, and it has caused a great deal of controversy. Many people (including PhD mathematicians) say switching should make no difference. Others say it should make a difference.
The correct answer is that you should switch, because it improves the probability of winning the car to 2/3. However, it is important to state your assumptions: Monty needs to know the location of the car, must always show a goat, must always allow a switch, and to make an informed choice, the contestant must be aware that this is the way the game is played.
Perhaps the simplest explanation is this: The probability that you picked a goat on your original guess is 2/3. Few will argue with that. So, 2/3 of time, when Monty shows you the location of the second goat, you're home free – the goat must be behind the remaining door. 2/3 of the time, you will win by switching.
From another perspective: Your chance of winning the car on your first guess is 1/3. Few will argue with that. If you do not switch, you have done nothing to change your chance of winning. So your probability of winning remains 1/3. Because you have only two choices (to switch or not), then the alternative probability (associated with switching) must be 2/3.
However, many people will say: "Wait!! When Monty shows a goat, that just reduces your choice to 1 of 2 options: there is a car behind one door, and a goat behind the other. The odds must be 5050." If you are in that group, you are in good company, and needn't feel bad. For those people, the "solution" is to read about the problem on the Web, and then, if unconvinced, to try out the 2 strategies using a simulator (many of which also exist on the Web). One of the best of these is graphically fun and allows you run many trials, seeing how the results stack up.

Re: Game Show Probability: Newsletter Challenge (05/01/07)