>>>No, it's correct. Review the truth table at
http://en.wikipedia.org/wiki/Monty_Hall_problem#Vos_Savant .
>>>
>>>If you're having trouble bending your mind around it, you're in good company.
>>>
>>>It's conditional probability - the end result is not an independent probability,
it depends on the results of prior choices.>>
>>Emphasis mine - it does not depend on
your prior choices. The probability changes because of the intervention of the host of the show - he knows what is behind all doors and he does not eliminate a door just at random. Instead, he specifically eliminates a door which he knows does not have the prize in order to be able to open it and show the goat. This changes the game and thus the odds as per the table you hyperlinked.
>
>I find the Carlton explanation elegant:
http://en.wikipedia.org/wiki/Monty_Hall_problem#CarltonIIRC, MythBusters also showed that people generally have a desire not to be shown as wrong, so they "defend" their initial choice and stick - even when they've heard this proof. While we've diverged onto the general topic of dumb things people do - I saw a demonstration of how to board passengers on a plane. Start at the back - window seats first. Even #'d rows. Then odd rows. The middle seats, even then odd, then aisle seats. With no practice this method beat the industry "standard practice" by two minutes. Unfortunately not adhering to the program leads to blockages. Standard practice is to assume we're all no smarter than ants and let us figure things out as we board.