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
>
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