You've probably heard this one before...

but my class spent yesterday afternoon grappling with "The Monty Hall Problem." I had seen it before but still had to prove it to myself all over again... both empirically, by setting up a version of it and playing it with friends, and logically.

There are three doors. Behind one door is a million dollars, behind another a goat, behind the third a horrible death. You don't know which door is which, and, like most people, you'd prefer the million dollars to death or a goat.

You choose a door.

Then Monty Hall (game show host) opens one of the other two doors and reveals the goat.

He gives you the option of staying with your original choice of doors, or switching to the final remaining door.

Which is a better strategy, staying or switching? And why?

Can you gather data in support of your strategy?

Is there a way to alter the game to make the two strategies equally good?

What was your thought process in solving this problem? Did you talk to friends about it? Was that helpful? What ideas about probability affected your thinking? Were they helpful?

By the way - this can be a very, VERY frustrating problem. There are logical-sounding arguments for both strategies (and for neither).