Common sense?
Wompom
We are presented with three doors-red, green, and blue-from which to choose,
one of which has a prize hidden behind it. Suppose we choose the red door.
The presenter, who knows where the prize is (and will not choose that door
to open), opens the blue door and reveals that there is no prize behind it.
He then asks if we wish to change our choice from our initial selection of
red. Will changing our mind at this point improve our chances of winning the
prize?
One might think that, with two doors left unopened, one has a 50:50 chance
with either door, and so there is no point in changing doors. However, this
is not the case.
ANSWER
we should always choose the green door. This assumes that the presenter
chooses at random
http://en.wikipedia.org/wiki/Bayes%27_theorem
"There are more things in heaven and earth, Horatio, than are dreamt of in
your philosophy"
W. Shakespeare, Hamlet
zenworm
"Behind The Green Door"
was that a movie?...
ZN ;D
jubilation for no reason owned by no one
Nobody in Particular
zenworm
well that kind of gives Wompom's answer:
"we should always choose the green door"
a whole 'nother artistic context...
:D
ZN
herbzet
Wompom wrote:
>
> QUESTION:
>
> We are presented with three doors-red, green, and blue-from which to choose,
> one of which has a prize hidden behind it. Suppose we choose the red door.
> The presenter, who knows where the prize is (and will not choose that door
> to open), opens the blue door and reveals that there is no prize behind it.
> He then asks if we wish to change our choice from our initial selection of
> red. Will changing our mind at this point improve our chances of winning the
> prize?
>
> One might think that, with two doors left unopened, one has a 50:50 chance
> with either door, and so there is no point in changing doors. However, this
> is not the case.
Since there are three doors, and the prize is behind a random door,
if we always stick with our original choice, we'll win 1/3 of the time.
Therefore, if we always switch, we'll win 2/3 of the time.
HTH.
--
hz
Nobody in Particular
http://en.wikipedia.org/wiki/Monty_Hall_problem
explains it very well, even with pictures for the math-challenged.
Marilyn vos Savant quotes cognitive psychologist Massimo Piattelli-
Palmarini as saying "... no other statistical puzzle comes so close to
fooling all the people all the time" and "that even Nobel physicists
systematically give the wrong answer, and that they insist on it, and
they are ready to berate in print those who propose the right answer."
... thinking of Feynman and his blind spot in regards to the
implication of quantum physics on the nature of reality.
norbu_tragri
"The Lady or the Tiger?" is a famous short story written by Frank R.
Stockton in 1882. Stockton later wrote a continuation of this story,
"The Discourager of Hesitancy". "The Lady or the Tiger?" has come into
the English language as an allegorical expression meaning an
unsolvable problem.
The semi-barbaric King of an ancient land utilized an unusual form of
administering justice for offenders in his kingdom. The offender would
be placed in an arena where his only way out would be to go through
one of two doors. Behind one door was a beautiful woman hand-picked by
the king and behind the other was a fierce tiger. The offender was
then asked to pick one of the doors, without knowing what was behind
it. If he picked the door with the woman behind it, then he was
declared innocent but was also required to marry the woman, regardless
of previous marital status. If he picked the door with the tiger
behind it, though, then he was deemed guilty and the tiger would rip
him to pieces.
One day the king found that his daughter, the princess, had taken a
lover far beneath her station. The king could not allow this and so he
threw the offender in prison and set a date for his trial in the
arena. On the day of his trial the suitor looked to the princess for
some indication of which door to pick. The princess did, in fact, know
which door concealed the woman and which one the tiger, but was faced
with a conundrum - if she indicated the door with the tiger, then the
man she loved would be killed on the spot; however, if she indicated
the door with the lady, her lover would be forced to marry another
woman, a woman that the princess deeply hated and believed her lover
has flirted with. Finally she did indicate a door, which the suitor
then opened.
http://en.wikipedia.org/wiki/Lady_or_the_Tiger
both stories are on line:
The Lady Or The Tiger:
The Final chapter:
How often, in her waking hours and in her dreams, had she started
in wild horror, and covered her face with her hands as she thought of
her lover opening the door on the other side of which waited the cruel
fangs of the tiger!
But how much oftener had she seen him at the other door! How in
her grievous reveries had she gnashed her teeth, and torn her hair,
when she saw his start of rapturous delight as he opened the door of
the lady! How her soul had burned in agony when she had seen him rush
to meet that woman, with her flushing cheek and sparkling eye of
triumph; when she had seen him lead her forth, his whole frame kindled
with the joy of recovered life; when she had heard the glad shouts
from the multitude, and the wild ringing of the happy bells; when she
had seen the priest, with his joyous followers, advance to the couple,
and make them man and wife before her very eyes; and when she had seen
them walk away together upon their path of flowers, followed by the
tremendous shouts of the hilarious multitude, in which her one
despairing shriek was lost and drowned!
Would it not be better for him to die at once, and go to wait for
her in the blessed regions of semi-barbaric futurity?
And yet, that awful tiger, those shrieks, that blood!
Her decision had been indicated in an instant, but it had been
made after days and nights of anguished deliberation. She had known
she would be asked, she had decided what she would answer, and,
without the slightest hesitation, she had moved her hand to the right.
The question of her decision is one not to be lightly considered,
and it is not for me to presume to set myself up as the one person
able to answer it. And so I leave it with all of you: Which came out
of the opened door - the lady, or the tiger?
http://www.eastoftheweb.com/short-stories/UBooks/LadyTige.shtml
The Discourager of Hesitancy
The tale is online here:
Toyah Willcox and Robert Fripp released a recording of "The Lady or
the Tiger?" and "The Discourager of Hesitancy" with Willcox reading
the stories to electric guitar accompaniment by Fripp.
http://en.wikipedia.org/wiki/Lady_or_the_Tiger
i highly recommend that recording - Toyah reads the text slowly, with
a hypnotic sensuality over the slow
string-section-like Bartok-like harmonies of Fripp bouncing a solo
electric guitar through tape loops.
Amazon has a few cassette copies and a couple used vinyl copies. i
have the Vinyl from 1986
if you were looking for an inexplicable unsettling inscrutable gift to
give slightly late for the holiday....
- n. (in front of the other door behind you)
Wompom
> http://en.wikipedia.org/wiki/Monty_Hall_problem
> explains it very well, even with pictures for the math-challenged.
> Marilyn vos Savant quotes cognitive psychologist Massimo Piattelli-
> Palmarini as saying "... no other statistical puzzle comes so close to
> fooling all the people all the time" and "that even Nobel physicists
> systematically give the wrong answer, and that they insist on it, and
> they are ready to berate in print those who propose the right answer."
>
> ... thinking of Feynman and his blind spot in regards to the
> implication of quantum physics on the nature of reality.
You know that Wikipedia aricle was just so excellently presented I bought
the company (OK that's a lie but I DID DONATE them �10 !)
Wompom
Toyah Willcox and Robert Fripp released a recording of "The Lady or
the Tiger?" and "The Discourager of Hesitancy" with Willcox reading
the stories to electric guitar accompaniment by Fripp.
http://en.wikipedia.org/wiki/Lady_or_the_Tiger
i highly recommend that recording - Toyah reads the text slowly, with
a hypnotic sensuality over the slow
string-section-like Bartok-like harmonies of Fripp bouncing a solo
electric guitar through tape loops.
Amazon has a few cassette copies and a couple used vinyl copies. i
have the Vinyl from 1986
if you were looking for an inexplicable unsettling inscrutable gift to
give slightly late for the holiday....
------------------------
How did you know?
:-)
herbzet
Nobody in Particular wrote:
>
> herbzet wrote:
> >
> > Wompom wrote:
> >>
> >> QUESTION:
> >>
> >> We are presented with three doors-red, green, and blue-from which
> >> to choose, one of which has a prize hidden behind it. Suppose we
> >> choose the red door. The presenter, who knows where the prize is
> >> (and will not choose that door to open), opens the blue door and
> >> reveals that there is no prize behind it. He then asks if we wish
> >> to change our choice from our initial selection of red. Will
> >> changing our mind at this point improve our chances of winning the
> >> prize?
> >>
> >> One might think that, with two doors left unopened, one has a 50:50
> >> chance with either door, and so there is no point in changing
> >> doors. However, this is not the case.
> >
> > Since there are three doors, and the prize is behind a random door,
> > if we always stick with our original choice, we'll win 1/3 of the
> > time.
> >
> > Therefore, if we always switch, we'll win 2/3 of the time.
> >
> > HTH.
>
> http://en.wikipedia.org/wiki/Monty_Hall_problem
> explains it very well, even with pictures for the math-challenged.
I apologize if my explanation was too complicated.
--
hz
Nobody in Particular
No problem. :-)
Actually, the reason for my reply was this quote in the Wikipedia
article:
"that even Nobel physicists systematically give the wrong answer, and
that they insist on it, and they are ready to berate in print those
who propose the right answer."
Some people simply cannot admit that they are wrong, and high
intelligence does not prevent that.
norbu_tragri
> "norbu_tragri" <norbu.tra...@gmail.com> wrote
>
> Toyah Willcox and Robert Fripp released a recording of "The Lady or
> the Tiger?" and "The Discourager of Hesitancy" with Willcox reading
>
> i highly recommend that recording - Toyah reads the text slowly, with
> a hypnotic sensuality over the slow
> string-section-like Bartok-like harmonies of Fripp bouncing a solo
> electric guitar through tape loops.
> Amazon has a few cassette copies and a couple used vinyl copies. i
> have the Vinyl from 1986
> if you were looking for an inexplicable unsettling inscrutable gift to
> give slightly late for the holiday....
>
> ------------------------
>
> How did you know?
>
> :-)
Well, i just looked for posterior distribution of the binomial
parameters,
then cross checked them for symmetry breaking, went back to the old
catastrophe theorems, reduced them to worms,
let them run for 60,000 hrs in sim, factored in Julian factors,
etc etc,
had some nice soup and garlic bread.
Then you just walk off into space...or not...
:)
Bayes post interesting - thanx!
zenworm
ah worms...
back to basics
ZN :D _/|\_
absolute permanent perfection overflowing without effort
Wompom
news:4B2C44EC...@gmail.com...
Good for you Mr.13% but have you shown it to your girlfriend recently?
Wompom
I presume that you are also aware that 1 is the same number as 0.999...
(All the nines recurring)
How else could it be so, as one third = 0.333...
Wompom
I get this one but my girlfriend swears she can't see it!
Wompom
news:713853fe-407d-441c...@u16g2000pru.googlegroups.com...
---------------------
Just as I had suspected!
:D
herbzet
I'm guessing you mean 13 inches.
I do take a certain pride in saying things as simply
and as clearly as I can.
It seems like a good thing to do.
--
hz
herbzet
Yes.
The standard way of conceptualizing this is to forget about
the *infinite* string of decimals, and look at the sequence
of *finite* decimals:
.9
.99
.999
.9999
.
.
.
and note that the difference between 1 and the sequence:
1 - .9
1 - .99
1 - .999
1 - .9999
etc.
will eventually get smaller than any positve number you choose.
The verbal shorthand for this fact is to say that 1 is the limit of the sequence
.9
.99
.999
.9999
.
.
.
and this is what is /meant/ by the shorthand notation .999...
The word "infinity" is completely avoided in this paradigm.
> (All the nines recurring)
>
> How else could it be so, as one third = 0.333...
Similar -- the sequence of *finite* decimals
.3
.33
.333
.3333
.
.
.
has the limit of 1/3; that is, the sequence
1/3 - 3/10
1/3 - 33/100
1/3 - 333/1000
1/3 - 3333/10000
etc.
will get smaller than any positive number you choose, eventually.
If this seems more complicated than the Monty Hall problem,
it's because it *is* more complicated. It took a couple of
hundred years for mathematicians to work it out rigorously.
So it's not quite fall-off-a-log simple.
http://www.sfbappa.org/clipcontest.images/07.6/feature/features_first.jpg
--
hz