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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/