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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. Apparently this created quite a stir surrounding Marilyn.
And for the record, IQ doesn't mean squat unless you can apply it
within subject matter. Especially important when it comes to physics
education. I can't tell you how many times I have heard that,
"Professor X is so smart that he/she can't come down to our level and
explain things." All that means to me is that Professor X can't
explain concepts.
Perhaps the best-known event involving vos Savant began with a
question in her 9 September 1990 column:
Suppose you're on a game show, and you're given the choice of three
doors. Behind one door is a car, behind the others, goats. You pick a
door, say #1, and the host, who knows what's behind the doors, opens
another door, say #3, which has a goat. He says to you, "Do you want
to pick door #2?" Is it to your advantage to switch your choice of
doors?
—Craig F. Whitaker Columbia, Maryland, [18]
This question, named "the Monty Hall problem" because of its
similarity to scenarios on the game show Let's Make a Deal, existed
long before being posed to vos Savant, but was brought to nationwide
attention by her column. Vos Savant answered arguing that the
selection should be switched to door #2 because it has a 2/3 chance of
success, while door #1 has just 1/3. Or to summarise, 2/3 of the time
the opened door #3 will indicate the location of door with the car
(the door you hadn't picked and the one not opened by the host). Only
1/3 of the time will the opened door #3 mislead you into changing from
the winning door to a losing door. These probabilities assume you
change your choice each time door #3 is opened, and that the host
always opens a door with a goat. This response provoked letters of
thousands of readers, nearly all arguing doors #1 and #2 each have an
equal chance of success. A follow-up column reaffirming her position
served only to intensify the debate and soon became a feature article
on the front page of The New York Times. Among the ranks of dissenting
arguments were hundreds of academics and mathematicians.[19]
Under the most common interpretation of the problem where the host
opens a losing door and offers a switch, vos Savant's answer is
correct because her interpretation assumes the host will always avoid
the door with the prize. However, having the host opening a door at
random, or offering a switch only if the initial choice is correct, is
a completely different problem, and is not the question for which she
provided a solution. Vos Savant addressed these issues by writing the
following in Parade Magazine, "...the original answer defines certain
conditions, the most significant of which is that the host always
opens a losing door on purpose. Anything else is a different
question." [20] In vos Savant's second followup, she went further into
an explanation of her assumptions and reasoning, and called on school
teachers to present the problem to each of their classrooms. In her
final column on the problem, she announced the results of the more
than a thousand school experiments. Nearly 100% of the results
concluded that it pays to switch. Of the readers who wrote computer
simulations of the problem, 97% reached the same conclusion. A
majority of respondents now agree with her original solution, with
half of the published letters declaring the letter writers had changed
their minds.[21]
Bill
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