Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] "Ask Marilyn"

New contributor here...

The best way I've found to encourage non-believing students to switch doors
in the Monty Hall problem involves limiting cases. Imagine there are 10, or
100, or 1000, or a million doors, only one of which hides a car. You pick
one door. Monty opens all the rest except 1 (so he opens 8, or 98, or 998,
or 999,998) and asks if you want to switch. Do you?

Students seem more comfortable convincing themselves to switch in this
case. The odds of picking the correct door from the outset seem incredibly
slim given the opportunity to take advantage of the new information Monty
presented by opening a bunch of doors. After convincing them to switch when
there are a million doors, well, what if there are 999,999? 999,998? Etc.

Then, of course, you can throw students the curveball of, say, having seven
doors, allowing them to pick 3, opening 3 of the remaining doors, and asking
them if they want to swap their 3 for the final unopened door that they did
not initially choose. Optimally, they should indeed trade their 3 doors for
that one unknown, but it's a bit counter intuitive until you realize that
you're actually trading 3 doors for 4 doors, but 3 of your new 4 have
already been opened. That doesn't change the probability that there was a
car behind there to start with, though.

Probability is wonderful.

Mike

On Wed, Jan 5, 2011 at 6:25 AM, Philip Keller <PKeller@holmdelschools.org>wrote:

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/



_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l
_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l