Monty Hall Problem

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I remember this coming up in a statistics class but I can't remember the details of it. Is the gist of it that you should swap the doors because it's assumed that your selected door is a goat because there are 2 goats and 1 car. Right?
[youtube]http://www.youtube.com/watch?v=mhlc7peGlGg[/youtube]

Yes, you should switch because the odds become 2/3 that you will get a car. It would take a picture for me to explain it better than how the stats teacher taught it.

However, IRL, the producers for Let Make a Deal would not let a situation like this occur.

I saw the pilot for the new Let's Make a Deal. It was terrible. I never saw the original but this plain stunk. Wayne Brady was hosting it so I don't know if that was the problem. For some reason, I find Brady to be really cheesy as a game show host.

Anyways, I wanted to make sure I had the right answer because I forwarded the youtube to someone and didn't want to screw them up with my explanation.

Definitely switch. Even though doing so is highly counterintuitive, it doubles your probability of winning.

Details are simple: At the start, there are three closed doors, so you have a 1:3 chance of selecting the door with a car behind it. If a door is opened and a goat is found, then the odds for the remaining two doors change because of this new information. The door you chose at the beginning keeps its 1:3 probability, but because there is only one door remaining, that door has a 2:3 in probability of having the car behind it. So switch and double your chances of winning.

The Monty Hall Problem is famous and old (you can find it in probability and combinatorics textbooks from the 80s and earlier), but became an international phenomenon when Marylin Vos Savant published it in her column. Famous mathematicians protested; even Paul Erdos was appalled. But she was proven right. The problem also appeared in an episode of the TV series "Numb3rs", but not in relation to the main plot.