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Re: [Phys-l] Monty Hall problem



Thank you John - this clears things up entirely for me.

I thought the discussion was continuing (as it had begun) with Marilyn's Parade column presentation of the 'Problem'. Each of these (that I have been able to peruse) was quite more limited than the long chart of scenarios that the wiki article covered.

Perhaps Marilyn's explanation was wanting but her response to the problem as stated in her column cannot be slighted. Her version(s) always included the host opening a goat door and offering a switch. Whether he had angelic or devilish intent is entirely irrelevant to the problem(s) as given in Parade magazine.

Her (correct) answer that one should always switch (Given the Parade version(s)) caused even more uproar among the readers of that column than has this pleasant exchange that has resulted here.

I thank everyone who has had to put up with my confusion.

Marilyn has made many mistakes/errors in her columns but her response to the problem as specified in her GameShow Column is not one of them.

Double your chance of winning by switching.
IIRC correctly this began with one of our members taking issue with her response on this.

Again - I thank you all for bearing with me in my time of confusion.
.
At 9:33 PM -0700 1/5/11, John Denker wrote:
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.
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