My son and I spent a little time this afternoon on the Monty Hall paradox, a topic we’d discussed a couple of years ago. Unfortunately, it takes me 20 minutes to understand the explanation, and I only understand it for 4 continuous seconds.

Here’s the situation. You are asked to pick one of three doors. Donkeys are behind two of them, and a new car is behind another. After you choose your door, but before it’s revealed to you, Monty Hall (the emcee) opens one of the doors you didn’t choose and reveals a donkey. He then asks if you’d like to switch from your initial choice to the remaining door. It turns out that if you agree to switch, you double (?) your chance of winning.

It just doesn’t seem possible. Here’s how one site, that has a simulator on it, explains it:

The easiest way to explain this to students is as follows. The probability of picking the wrong door in the initial stage of the game is 2/3. If the contestant picks the wrong door initially, the host must reveal the remaining empty door in the second stage of the game. Thus, if the contestant switches after picking the wrong door initially, the contestant will win the prize. The probability of winning by switching then reduces to the probability of picking the wrong door in the initial stage which is clearly 2/3.

Despite a very clear explanation of this paradox, most students have a difficulty understanding the problem…

Yeah, that was real clear. Oh yeah.

The only explanation that’s ever worked for me is the 1,000 door variation, which you can find here. And here’s the front page NY Times story about it.

Now please don’t bring this up for another two years. It’s given me a headache. [Technorati tags: paradox puzzle]

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