Here is a simple way to explain without simulation, or increasing door count, and which breaks the illusion of symmetry.
Clearly, Monty starts with a 2/3 chance of having the prize, and you start with 1/3. Then he always offers you the best of his doors, which is the same thing as offering you both doors and allowing you to look behind both of them before choosing one. It is just that he has peeked behind for you.
So, the doors are not all the same because the door he offers is a "best of two" door.
With regard to the point of the editorial, I think this problem illustrates that controversies will continue either until someone sees a way of explaining things so clearly they are widely understood, or until the general level of sophistication and collateral/related knowledge rises to the point where the large majority of interested people can understand the matter. Both phenomena happen over time. In areas where neither happens, there remain controversies and a struggle for clarity should continue.
posted by Tanj Bennett
September 4, 2008
Check out our most recent podcast: How You Can Better Communicate Your Science - science author and journalist Dennis Meredith discusses some of the ways he’s found to help scientists become more effective communicators.
Click the Title to view all of our Pizza Lunch Podcasts!
A free daily summary of the latest news in scientific research. Each story is summarized concisely and linked directly to the original source for further reading.
An early peek at each new issue, with descriptions of feature articles, columns,
and more. Every other issue contains links to everything in the latest issue's table of contents.
News of book reviews published in
and around the web, as well as other noteworthy happenings in the world of science books.
To sign up for automatic emails of the
Update and Scientists' Nightstand issues, create an
online profile, then sign up in the
My AmSci area.