Re: [Phys-l] "Ask Marilyn"

[Philip Keller <PKeller@holmdelschools.org>]

There are also MANY sites devoted to this topic on the web, including sites with simulations.  

For example:  http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/monty.hall.applet.html

BTW, I found these by google-searching for "Monty Hall applet".  It is amazing how much useful stuff you find when you add the word "applet" to your search string.
________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-bounces@carnot.physics.buffalo.edu] on behalf of Brian Blais [bblais@bryant.edu]
Sent: Wednesday, January 05, 2011 5:49 AM
To: Forum for Physics Educators
Subject: Re: [Phys-l] "Ask Marilyn"

On Jan 5, 2011, at 12:09 AM, William Robertson wrote:

> The following is from Wikipedia, regarding a puzzle that was answered
> by Marilyn. I'm not seeing the advantage of switching choices, because
> once you have new information, a new choice is made, which seems to me
> to be 50-50.

The very best way I've found of convincing yourself that the 2/3 answer is the correct one is to write a simple computer program to simulate the system.  I remember doing that in college, when I wasn't convinced, and I never finished the program because the result became so obvious somewhere between 1/2 to 2/3 through writing it.  :)

The key thing here is to realize, in the simulation, is the following:

* say the prize is behind door 2 (you can repeat this logic with the other possibilities later)
* you're asked for a door, and you choose 1
* the game show host is constrained - he must open an empty door, and he must not open your door (empty or not)
        * the host, in this case, **must** open door 3 - given his information, his choice provides you with a little
* you can then re-guess

if you make a simulation of this, you'll see quickly what the right answer is.  it's very easy to convince yourself of *either* answer from various manipulations of the probabilities.  A simulation can be a bit more intuitive here.

Although it is pretty simple, a python simulation of this can be found on my blog, here:

        http://bblais.blogspot.com/2009/09/probability-problems-and-simulation.html

                        bb

--
Brian Blais
bblais@bryant.edu
http://web.bryant.edu/~bblais
http://bblais.blogspot.com/



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