Don't think allstat is the place to have the whole thing dragged out
again. It's a great problem though.
There are a few other related problems on
http://en.wikipedia.org/wiki/Monty_Hall_problem#Similar_problems
if you've some downtime on your hands.
>>> Fen Scott <[log in to unmask]> 11 June 2008 11:42 >>>
Hi folks.
In my opinion you can disregard the first door opened as it will ALWAYS
be a
goat, and therefore any earlier probabilities can also be ignored. This
is,
in essence, a two door game. So the door you chose has a 50/50 chance
of
being the prize door. Therefore swapping is immaterial.
Cheers,
Fen.
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Kate Harper
> Sent: 11 June 2008 11:14
> To: [log in to unmask]
> Subject: Re: Goat problem solution
>
> I'm no expert on this but;
>
> If there are 3 doors and only one has a car then you have 2/3 chance
of
> choosing a door with a goat at the first step.
>
> Now, at the second stage, when there are two doors, if you switch
you
> must either move "from goat to car" or "from car to goat".
>
> If there is a 2/3 chance that you have a goat from the first round
and
> switching when you have a goat guarantees you get the car then there
is
> a 2/3 chance that to swap gives you the car and to stick gives you
the
> goat.
>
> You should swap!
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Mario Ouwens
> Sent: 11 June 2008 10:04
> To: [log in to unmask]
> Subject: Goat problem solution
>
> Dear all,
>
> I want to add a simple comment, which explains a lot to me. Suppose
3
> boxes
> A, B, C and suppose that a priori the chance is equal for the three
> boxes.
> Then
>
> P(A) = P(B) = P(C) = 1/3.
>
> Now suppose you choose A. Then the chance you are right is equal to
> 1/3.
>
>
> If it is A, B or C is opened. The switch will end up in the wrong
> result.
> If it is B, C will be opened. The switch is to C and will result in
the
> right result.
> If it is C, B will be opened. The switch is to B and will result in
the
> right result.
>
> What happens is that in the second case and the third case,
different
> boxes
> are opened. So, the chosen box when you switch is different, while
in
> the
> case you do not switch, you stay in the first situation, regardless
the
> additional information. Hence, you use the information that the
other
> box is
> not the right one.
>
> Best wishes,
>
> Mario Ouwens
>
>
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of John Bibby
> Sent: Wednesday, June 11, 2008 10:41 AM
> To: [log in to unmask]
> Subject: Re: Goat Problem
>
>
> One way which I think is sound and shows that you should shift
> (although
> it
> does not provide any numbers) is the following:
>
> Consider the choice as a two-stage problem:
> D1: choose a door
> D2: Should I shift, and if so to which one?
>
> Suppose you decide D1 and D2 simultaneously on the basis that NO
door
> will
> be opened.
>
> Then 'clearly', D1+D2=shift has just the same chances as D1 alone
(i.e.
> D1+D2=noshift)
>
> Now if a door is opened to show a goat. This HAS to increase the
chance
> of
> getting the prize if you shift. So D2=shift is preferable to
> D2=noshift.
>
> QED
>
> JB
>
> -----Original Message-----
> From: A UK-based worldwide e-mail broadcast system mailing list
> [mailto:[log in to unmask]] On Behalf Of Rob Fitzmaurice
> Sent: 10 June 2008 09:15
> To: [log in to unmask]
> Subject: Re: Goat Problem
>
> I didn't see the previous discussion but this offers some thoughts:
>
> http://montyhallproblem.com/
>
> Rob
>
>
> >
> > From: John McKellar <[log in to unmask]>
> > Date: 2008/06/10 Tue AM 07:37:07 GMT
> > To: [log in to unmask]
> > Subject: Goat Problem
> >
> > 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
> >
>
> -----------------------------------------
> Email sent from www.virginmedia.com/email
> Virus-checked using McAfee(R) Software and scanned for spam
> DISCLAIMER: The information in this message is confidential and may
be
> legally privileged. It is intended solely for the addressee. Access
to
> this
> message by anyone else is unauthorised. If you are not the intended
> recipient, any disclosure, copying, or distribution of the message,
or
> any
> action or omission taken by you in reliance on it, is prohibited and
> may
> be
> unlawful. Please immediately contact the sender if you have
received
> this
> message in error. Thank you.
>
>
______________________________________________________________________
> This email has been scanned by the MessageLabs Email Security
System.
> For more information please visit http://www.messagelabs.com/email
>
______________________________________________________________________
>
> The information contained in this E-mail is confidential. It is
> intended only for the stated addressee(s) and access to it by any
other
> person is unauthorised. If you are not the addressee, you must not
> disclose, copy, circulate or in any other way use or rely on the
> information contained in this E-mail. Such unauthorised use may be
> unlawful. If you have received this E-mail in error, please inform
us
> immediately and delete it and all copies from your system. Emails
> containing CV's are subject to our standard terms of business.
> Acceptance of CV's constitutes acceptance of our terms of business
> unless otherwise agreed in writing.
>
> Astbury Marsden & Partners is registered in England and Wales and
> holds company registration number 3318173. Its registered office is
> located at Augustine House, 6a Austin Friars, London, EC2N 2HA
>
>
______________________________________________________________________
> This email has been scanned by the MessageLabs Email Security
System.
> For more information please visit http://www.messagelabs.com/email
>
______________________________________________________________________
|