MY AMERICAN SCIENTIST
SEARCH

HOME > ON THE BOOKSHELF > COMMENTS > Comment Detail

Monty Hall Redux

Comment

Brian states: "The issue is how I can persuade anyone that my answer—or any particular answer—is correct."

Here's another attempt to provide an intuitive insight into why 2/3 is the correct answer...

Suppose there are 100 doors, and all other conditions of the original 3-door puzzle remain intact.

The player chooses one door.

Would everyone agree that the chances of the prize being behind one of the remaining 99 doors is 99/100 ? (And, that the door chosen by the player has only a 1 in a 100 chance of containing the prize?)

"Monty" opens 98 of the remaining 99 doors.

What do you think the chances are of the prize being behind that one door that "Monty" did not open ?

99 to 1, or 1:1 (50/50) ?

I think you'd have a strong feeling that the chances are 99:1, and that you should switch doors. Right ?

Apply that same logic ("feeling") to the 3-door situation and you are left with the choice:

2:1 or 1:1 ?

It seems then, applying the same logic, that the 2:1 odds apply to that remaining unopened door, and that switching doors would be in your best interest.

Hope this analogous problem helps some of you get by the mind-bending nature of the 3-door problem.

Peter

posted by Peter Rauch
August 25, 2008

Pizza Lunch Podcasts

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!

Subscribe to Free eNewsletters!

• Sigma Xi SmartBrief:

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.

• American Scientist Update

• An early peek at each new issue, with descriptions of feature articles, columns, Science Observers and more. Every other issue contains links to everything in the latest issue's table of contents.

• Scientists' Nightstand

• News of book reviews published in American Scientist and around the web, as well as other noteworthy happenings in the world of science books.

To sign up for automatic emails of the American Scientist Update and Scientists' Nightstand issues, create an online profile, then sign up in the My AmSci area.