re: Marilyn vos Savant and the history of the Montel Hall question

quote:

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I'm with you since I"m not a math/probability guy AT ALL, but how someone explained it to me was this.

At the start when you pick a door, you have a 33% chance of guessing correctly. After 1 door is revealed to be nothing, now your chances of picking the correct door are 50/50 between car and goat, so you're "supposed" to switch. I don't really get it, but that's how it was told to me.

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Look at it this way:

There are 3 doors. You pick door 1. The host says, "You can either keep door 1 or have BOTH of the the other doors."

You know for sure that at least one of these other two doors have a goat behind it, but you will still make the switch because two doors are better than one.

The actual problem follows the same logic.
You pick a door, and then are given the option of keeping your door or switching to the other 2 doors. The only difference is that this time they show you that one of the other two doors has a goat behind it...but you already knew with certainty that one of these two doors had a goat behind it, so him showing it to you doesn't change anything.