Brain teaser

I saw this Monty Hall paradox on the Ace of Spaces blog, but the answer really bugged me for awhile.  Now I think I can accept the answer as true.  If you aren't familiar, here's the video explaining the problem.



Comment:

The answer given in the above video didn't satisfy me, so I went on the web to look for an answer that would. I still didn't accept it after reading over many explanations and so forth. But when I read about the option of expanding to 1,000,000 ( 1 million) doors, it then struck me that the answer that I wouldn't accept was true after all.

That's because the probability of getting the correct door out of 1 million doors is 1 in a million. If all the incorrect doors are removed from consideration and then you are asked if you want to switch to the last remaining door, the odds are not 50-50 that the remaining door is the incorrect one and that the one you originally chose was the correct one all along. Since certainly it must true in that case, it must also true in the case of only 3 doors.

Getting to that point was not easy for me to accept.  The truth is really slippery after all.