Re: [Phys-l] Monty Hall problem

[John Denker <jsd@av8n.com>]

On 01/05/2011 09:00 PM, chuck britton wrote:
> Each Marilyn scenario that I have read includes the host opening a
> goat door and offering a switch.
> Have I missed one?


I don't know what a "Marilyn scenario" is or how it differs
from any other kind of scenario.

More importantly, the fact remains that there are plenty of
real-world scenarios where Monty did not open a door and
did not offer a switch.  Indeed this are not just scenarios
but well-attested reports of actual occurrences.  It is 
really quite silly to say it could not happen this way, 
when it did in fact happen.

Marilyn's analysis is wrong precisely because she failed to
consider all of the plausible scenarios.

If you insist on considering only "Marilyn scenarios" you
require yourself to make the same mistake did.

This connects to Marilyn in that the actual original question
that she actually published is open to far more reasonable
interpretations than the one chose to consider.

By way of analogy:  I am fond of assigning the following
question:  Given that x^2 is 81.  
  a) What is x?
  b) How do you know, and how sure are you?

It's quite amazing how many people are absolutely sure 
that x=9.  They would stake their life on it.  Alas, if
x happens to be -9, they would lose their life.

The fundamental problem is this:  Just because you have
one way of answering the problem, that is not necessarily
the only way of answering the problem.  In general there
is a _solution set_.  It is quite foolish to assume that
the solution set contains only one element.

In the real world, it is not uncommon to find x = -9.  
You can "assume" x is positive, but if so you are making
a wrong assumption.  If your assumption is the same one
that Marilyn made, it is still a wrong assumption.

If you insist on making wrong assumptions, you can obtain
any result you like, and be absolutely certain of your
results.