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• ##### My explanation(4+ / 0-)
Recommended by:
plf515, guyeda, NCrissieB, Toon

goes like this:

First, you divide the doors into Chosen and Unchosen groups.

Second, list what you know about each group. The Chosen group has 1 door which has a 1/3 chance of having the car and a 2/3 chance of having a goat. The Unchosen group has 2 doors. As a group, it has a 100% chance of having a goat, a 2/3 chance of having the car and a 1/3 chance of having a second goat.

Third, understand that the group odds above remain until you get new information about a group as a whole.

Fourth, when Monty opens a door, he always opens a door with a goat in the Unchosen group. This is not new information about the Unchosen group since you already knew the group had a 100% chance of having a goat. The group still has a 2/3 chance of having the car and a 1/3 chance of having a second goat. The only new information Monty has provided is internal to the Unchosen group, letting you claim the full 2/3 odds of getting a car by changing your pick to the single unopened door of that group.

Deranged neoconservative militarism isn't the solution to nuclear proliferation; it's a cause. -- Glenn Greenwald

• ##### Nice. I tried that tack above, but I think(3+ / 0-)
Recommended by:
plf515, factbased, NCrissieB

your explanation is better. That works assuming Monty always offers the new deal.  What if he doesn't always offer a new deal? What if from an analysis of Monty's past behavior you determine that about 2/3rds of the time, he offers the new deal only when the chooser has chosen the car the with his first choice.  How does this affect the thinking?  Has the probability now collapsed to a 50/50 choice?

• ##### Thanks(1+ / 0-)
Recommended by:
NCrissieB

I've explained it several ways over the years and that's the one that makes it most obvious to me. Sometimes I do the 100 doors. Or just say pick a number between 1 and a million and see if it matches the number I write down. Then narrow it down to 2 numbers. Do you want to stay with your number or switch to 247117?

I replied to your post further up. I think I followed the new rule you used up there, but I'm not sure I understand the way you state it here.

Deranged neoconservative militarism isn't the solution to nuclear proliferation; it's a cause. -- Glenn Greenwald

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