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

Let me try explaining it this way.

Pretend you are the contestant and you make your pick first between the three doors.

Everyone agrees that at this point you have a 1/3 chance to win.

Ok now let's say I get to pick both of the remaining two doors that you didn't pick.

Can everyone agree that I have 2/3 chance of winning the prize to your 1/3?

That is the same thing as allowing Monty to eliminate the one door out of the two remaining that doesn't have the prize behind it.

Exactly the same odds.

quote:

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blows me away that college educated people cannot immediately see that

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Meh, it certainly isn't an obvious answer.

I like to break it down much further than 3 doors. Imagine 100 doors - 99 goats and 1 car - Door #37. You choose Door #42. Monty opens the other 98 doors leaving you with your choice and #37. Basically, if you stay, you're saying the other 98 doors being opened were irrelevant, because you stayed with your original choice. If you switch, your effectively giving yourself the chance to see 99 doors get opened, hence your chance of winning is 99% if you switch, and only 1% if you stay.