Monty Hall Problem

I found the easiest way to convince non-mathematical types is by suggesting we do the million-door version: “Ok, pick a door between 1 and 1,000,000. We’ll call that door N. Now, I’ll open 999,998 bad doors. So, now only door N and door 223,205 are still closed, and one of them has the good prize. Want to keep door N, or swap?”

The fact that the show host knows what's behind the doors and never chooses a door with the prize behind it is crucial. The host leaks information about what's behind, as he chooses a door. I was told about this problem and the person telling it didn't say anything about that, just that you pick a door and the host opens another one which doesn't have a prize behind it. So I thought the probabilities don't change at all because…

I always find this the most interesting part of it: "A restated version of Selvin's problem appeared in Marilyn vos Savant's Ask Marilyn question-and-answer column of Parade in September 1990 (vos Savant 1990). Though vos Savant gave the correct answer that switching would win two-thirds of the time, she estimates the magazine received 10,000 letters including close to 1,000 signed by PhDs, many on letterheads of mathematics and science departments, declaring that her solution was wrong (Tierney 1991). " Especially…

Good topic, I posted my take on the Monty Hall problem on my blog: http://jacobirw.wordpress.com/2011/12/11/the-monty-hall-prob...