See http://en.wikipedia.org/wiki/List_of_paradoxes#Probability, but none of
the others are as much fun.
What makes Monty Hall so good is the positive relationship I've observed
between the academic qualifiications of the subject and the probability that
they get the puzzle wrong, and also with the vehemence with which they
insist on the wrong answer. It's perfect for the Departmental Coffee Room
(where these still exist!). To quote Wikipedia quoting von Savant quoting
Massimo Piatelli-Palmarini: "... no other statistical puzzle comes so close
to fooling all the people all the time" and "[realize] 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."
Mike Weale
----- Original Message -----
From: "John Bibby" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, June 10, 2008 9:39 PM
Subject: Re: Goat Problem
> I'm intrigued by a rather different goat question (some wd call it a
> meta-goat):
>
> What is it about this problem that makes it so appealing?
>
> Is it the fact that it refers to a TV show that none of us (in the UK)
> have
> heard of, or does it have some other intriguing feature?
>
> If the latter, can we generalise - i.e. what other problems have this same
> feature?
>
> JOHN BIBBY
>
> PS: BTW, the Wikipedia article changes many times each week. A couple of
> years ago I tried to "correct" it, but I gave up because too many
> dunderdasses were instantly re-editing my edits. (I find Wikipedia
> reliable
> on many things and a great source - but not on Monty Hall)
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Breukelen v Gerard (STAT)
> Sent: 10 June 2008 14:49
> To: [log in to unmask]
> Subject: FW: Goat Problem
>
> Hi Allstat members,
>
> It seems that the classical quiz master (goat) problem keeps several
> list members quite busy. To me this once more shows the importance of
> formalized instead of informal thinking. So below is my result, using
> Bayes' theorem
> (too simple not to have been produced by someone else somewhere else
> before, I guess). See if you can find an error in it.
>
> Kind regards,
> Gerard van Breukelen
> Maastricht University, The Netherlands
>
>
> -----Original Message-----
> From: Breukelen v Gerard (STAT)
> Sent: dinsdag 10 juni 2008 15:40
> To: 'Iain Third'
> Subject: RE: Goat Problem
>
> Hi Ian,
>
> I am sorry to disagree with you. Using Bayes theorem shows that whether
> the quiz master knows or does not know the right door, makes the big
> difference between a posterior probability of 33% or 50% for the
> candidate to have made the right choice. Below is the proof. See if you
> can find an error there.
>
> Best regards,
> Gerard van Breukelen
> Maastricht University, The Netherlands
>
>
> Define the following events:
>
> A = candidate chooses the right door (with the car behind it), P(A) =
> 1/3
> a = candidate chooses a wrong door (with a goat), P(a) = 2/3
> B = quiz master opens the right door,
> b = quiz master opens a wrong door
>
> Bayes theorem: P(A|b) = P(A) * P(b|A) / P(b)
>
> with:
>
> P(A|b) = posterior probability that candidate chose the right door,
> given that quiz master has opened a wrong door.
>
> P(b|A) = probability that quiz master opens wrong door,
> given that the candidate chose right door = 1.
>
> P(b) = prob that quiz master opens wrong door = P(A)*P(b|A) +
> P(a)*P(b|a).
>
> We already know:
>
> P(A) = 1/3
> P(a) = 2/3)
> P(b|A) = 1
>
> Crucial now is P(b|a) = prob that qm opens wrong door given that
> candidate chose wrong door.
>
> Assumption 1: qm knows right door and will never open it, so P(b|a) = 1.
> This gives P(b) = 1 and so P(A|b) = {1/3 * 1} / 1 = 1/3,
> So the posterior prob that the candidate chose rightly, given that qm
> has opened a wrong door, is 1/3 only.
>
> Assumption 2: qm does not know the right door and choses randomly
> between the two non-chosen doors, so P(b|a) = 1/2. This gives P(b) = 2/3
> and so P(A|b) = {1/3 * 1} / 2/3 = 1/2,
> So the posterior prob that the candidate chose rightly, given that qm
> has opened a wrong door, is 1/2 in line with intuition.
>
> Now given a sequence of quizes in which the qm has never opened the
> right door, assumption 1 is very likely to be correct, giving the
> posterior probability 1/3 for the candidate to have chosen correctly.
> In the very first quiz, however, we cannot tell which assumption is
> correct.
> But even then the candidate had better switch to the third door if he
> chose the first one and the qm opens the 2nd one, finding a goat there.
> After all, switching is wise if assumption 1 holds and does not matter
> if assumption 2 holds.
>
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Iain Third
> Sent: dinsdag 10 juni 2008 14:57
> To: [log in to unmask]
> Subject: Re: Goat Problem
>
>
> The wikipedia reference on this has a section on alternate scenarios
> which I am convinced is wrong.
>
> It states that if after you have made your initial pick, the presenter
> forgets which door has the car behind it, and so goes for broke and
> luckily picks a door with a goat behind it, the odds are now 50/50 as to
> whether switching gives the car or not. To me it shouldn't matter what
> the presenter knows or doesn't know, only the information he reveals
> once he has opened the door.
>
> Granted, there is a 33% chance he will muck things up and open the door
> with the car, but after that stage, if he got a goat, nothing changes,
> and the odds should still be 0.66 if you switch, 0.33 if you don't.
>
> The references are Granberg and Brown, 1995:712 and vos Savant, 2006
> which I have not read so I could be misenterpreting them.> Date: Tue, 10
> Jun 2008 10:52:35 +0300> From: [log in to unmask]> Subject: Re: Goat
> Problem> To: [log in to unmask]> > John McKellar wrote:> > Call me
> stupid, but I've just heard the 3 door game show on a> > discussion
> about probability on radio BBC4's Material World, and I think> > it was
> also discussed by Mervyn Bragg (sorry very UK-centric) this week.> >> >
> My problem is I don't believe the discussion. BUT I suspect it's an old>
>> topic here, so rather than generate the same again;> > Does anyone
> have a clear discussion on the problem from last time?> >> > John> >
> --------------------------> > John McKellar> >> >> > > Hi John,> > maybe
> this can help:> > http://en.wikipedia.org/wiki/Monty_Hall_problem> > >
> -- > Nikolaos A. Patsopoulos, MD> Department of Hygiene and
> Epidemiology> University of Ioannina School of Medicine> University
> Campus> Ioannina 45110> Greece> Tel: (+30) 26510-97804> mobile: +30
> 6972882016> Fax: (+30) 26510-97853 (care of Nikolaos A. Patsopoulos)>
> e-mail: [log in to unmask]
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