Even after she explained it she still received so many replies saying she was wrong, I just am wondering what's going on here that's causing this. That's just so bizarre.
It's actually a really big cognitive leap to get from there to the idea that, because the gameshow host knows the answer, that the visible answer differs from the mental shortcut.
I've got a good friend who speaks at a lot of risk management seminars, and a good deal of people who deal with financial risk every day get this question wrong. He's got a really good blog at http://behavioralrisk.net/
Yes. The difficulty with the Monty Hall problem has to do with grasping all the probabilities represented by all the outcomes at once. I personally didn't fully understand it until I wrote a list of all the possible outcomes and summed the probabilities.
I found her matrix rather messy & convinced myself with the following:
| chosen | revealed | hidden |
| car __ | empty __ | goat__ |
| empty_ | goat ___ | car __ |
| goat _ | empty __ | car __ |