Sciam - cover

From the February 2009 Scientific American Magazine | 52 comments

The 3-Door Monty Hall Problem

Michael Shermer's extended response to a question about the Let's Make a Deal Skeptic column

 
e-mail print comment

I find amazing that serious scientists like Robert Plomin and others quoted in Carl Zimmer’s review article keep looking for genes related to a nonentity such as intelligence. Haven’t we known for some time that the usual notion of intelligence is a pure psychometric fiction (g factor, etc.) ?  What the cognitive neurosciences are demonstrating is the existence of a number of “intellectual” or better cognitive functions, largely dissociated as the pathologies show. These functions and the knowledge stored (factual, procedural) are but the product of a very long chain of interactions between some aspects of the genotype and environmental factors from conception on. These processes are associated likely with a large number of “structural” genes (as suggested by the studies on the congenital genetic conditions leading to cognitive disabilities. There is no mystery involved here ‘as Zimmer seems to imply (rather stupidly in my view). Just that people  must look at the right place :cerebral structures and interindividual  variations at that level (as some researchers have started to do) and certainly not at the mere products. In this sense, the failure of Plomin and others to identify so-called intelligence genes was highly predictable.
 
Sincerely,
Dr. J.A. RONDAL, Ph.D., Dr. Sc. Lang.
Professeur Ordinaire Emérite de l'Université de Liège
Professeur à l'Université Pontificale salésienne de venise
Privé:
118 FRAITURE
4140 SPRIMONT
BELGIQUE

The 3-Door Monty Hall Problem
By Michael Shermer

In nearly 100 months of writing the Skeptic column I have never received so many letters as I did in response to my October essay (“A Random Walk Through Middle Land”) on the so-called Monty Hall Problem: you are on a game show with three doors, behind one of which is a car and behind the other two are goats. You pick door #1. Monty, who knows what’s behind all three doors, reveals that behind door #2 is a goat. Before showing you what you won, Monty asks if you want to switch doors. Most people say that it doesn’t matter because it is now a 50/50 choice. I explained that you should always switch. My correspondents disagreed.

The James Madison University mathematics professor Jason Rosenhouse, who has written an entire book on the subject—The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brainteaser (Oxford University Press, 2009)—explained to me that you double your chances of winning by switching doors when three conditions are met: (1) Monty never opens the door you chose initially; (2) Monty always opens a door concealing a goat; (3) When the first two rules leave Monty with a choice of doors to open (which happens in those cases where your initial choice was correct) he makes his choice at random. “Switching turns a loss into a win and a win into a loss,” says Rosenhouse, “and since my first choice is wrong 2/3rds of the time, I will win that often by switching.”

Here’s why: At the beginning of the game you have a 1/3rd chance of picking the car and a 2/3rds chance of picking a goat. Switching doors is bad only if you initially chose the car, which happens only 1/3rd of the time. Switching doors is good if you initially chose a goat, which happens 2/3rds of the time. Thus, the probability of winning by switching is 2/3rds, or double the odds of not switching (keeping in mind the three rules above). Analogously, if there are 10 doors, initially you have a 1/10th chance of picking the car and a 9/10ths chance of picking a goat. Switching doors is bad only if you initially chose the car, which happens only 1/10th of the time. Switching doors is good if you initially chose a goat, which happens 9/10ths of the time. Thus, the probability of winning by switching is 9/10ths, again, assuming that Monty has shown you 8 other doors with goats.



Read Comments (52) | Post a comment 1 2 Next >


Share
Propeller    Digg!  Reddit delicious  Fark 
Slashdot    RT @sciam The 3-Door Monty Hall ProblemTwitter Review it on NewsTrust 
sharebar end

You Might Also Like


Discuss This Article


Click here to submit your comment.

VIEW:

2,573 characters remaining
 
  Email me when someone responds to this discussion.
 

risk free issuefree gift

Sciam - cover Email:
Name:
Address:
Address 2:
City:
State:  
spacer




Editor's Pick

  • Adapting to the Freshwater CrisisForward-thinking experts are getting a better handle on the growing global water shortage and coming up with innovative approaches to ensuring the security, safety and sustainability of this resource

Newsletter

Basic Science Newsletter

Get weekly coverage delivered to your inbox


 Podcasts

  • 60-Second Earth     RSS  · iTunes The Jellyfish Menace
    click to enable

    Download

  • 60-Second Science     RSS  · iTunes Plants Share Light If Neighbor Is Related
    click to enable

    Download





ADVERTISEMENT
 
 


Also on Scientific American


© 1996-2009 Scientific American Inc. All Rights Reserved. Reproduction in whole or in part without permission is prohibited.
ADVERTISEMENT