I like it. Option C contains 2 possibilities C: Got the car this time, the presenter shows that there is a goat behind door 2 (or 3) Stay - Car Swap - Goat
or look at it this way: The combination matrix is actually like this: (With 2 goats) G1 G2 C G2 G1 C G1 C G2 G2 C G1 C G1 G2 C G2 G1 Your change of being right first time is ~.333 I follows that the presenter has a probability ~.666 of having to eliminate the second goat. So swap to the ~.666 probability > > I thought I had a good explination > > > > Here is my table again > > A: G G C > > B: G C G > > C: C G G > > > > A: represents Goat behind doors 1 & 2 and Car behind Door 3 > > > > Lets continue to assume that we still always pick door number 1 > > > > A: We've chosen a goat (however we don't know this). The presenter > > will now tell us that there is a goat behind door 2. What > happens if we > > stay or swap? > > Stay - Goat > > Swap - Car > > > > B: Still chosen a goat, the presenter shows us that there is a goat > > behind door number 3. And again here is what happens if we > stay or swap. > > Stay - Goat > > Swap - Car > > > > C: Got the car this time, the presenter shows that there is a goat > > behind door 2 (or 3) > > Stay - Car > > Swap - Goat > > > > So if we stay we get Goat, Goat, Car, thus 1 out of 3 times > we get the > car. > > > > If we swap we get Car, Car, Goat - 2 out of 3 times we get the car. > > > > The same arguments apply if we initially chose door 2 or door 3. > > > > I hope this explination makes things clearer. I think the main > > confusion is from trying to assign probabilities. If I've missed > > something and am wrong then will somebody explain my confusion in > > language simple enough so that I can understand it ;-) > > > > However I think that the test applications also show that > the answer is > > correct even if my reasoning is wrong. > > > > Alister > > > > > > Paul M - ProSouth wrote: > > > Ok, if he opens door 2 to reveal the goat, we now know > that option B > (GCG) > > > is incorrect, leaving: > > > > > > A: G G C > > > C: C G G > > > > > > Again, a 50/50 scenario. > > > > > > Regards, > > > > > > Paul Matthews > > > ProSouth Technology Solutions > > > Phone: +64 3 470 1321 > > > DDI: +64 3 470 1324 > > > 0800 PROSOUTH (0800 776 768) > > > 249 Cumberland Street, Dunedin, New Zealand > > > Visit us at www.prosouth.co.nz > > > > > > ----- Original Message ----- > > > From: "Stacey Verner" <[EMAIL PROTECTED]> > > > To: "NZ Borland Developers Group - Delphi List" > <[EMAIL PROTECTED]> > > > Sent: Thursday, August 05, 2004 2:11 PM > > > Subject: RE: [DUG] Welcome back problem > > > > > > > > > > > >>We aren't assuming that he opens door 3. He will open a > door with a > > >>goat, which in case A is door 2. > > >> > > >>Stacey > > >> > > >> > > >>>-----Original Message----- > > >>>From: [EMAIL PROTECTED] > > >>>[mailto:[EMAIL PROTECTED] On Behalf Of Paul > M - ProSouth > > >>>Sent: Thursday, 5 August 2004 14:03 > > >>>To: NZ Borland Developers Group - Delphi List > > >>>Subject: Re: [DUG] Welcome back problem > > >>> > > >>> > > >>>What you are ignoring is the additional information. > > >>> > > >>>Using your matrix, the host opens door 3 to reveal a goat. > > >>>This now removes Option A, G G C, as being a > possibility, leaving: > > >>> > > >>>B: G C G > > >>>C: C G G > > >>> > > >>>There is now a 50% chance that the car is behind door 1 or 2. > > >>> > > >>>Regards, > > >>> > > >>>Paul Matthews > > >>>ProSouth Technology Solutions > > >>>Phone: +64 3 470 1321 > > >>>DDI: +64 3 470 1324 > > >>>0800 PROSOUTH (0800 776 768) > > >>>249 Cumberland Street, Dunedin, New Zealand > > >>>Visit us at www.prosouth.co.nz > > >>> > > >>>----- Original Message ----- > > >>>From: "Alister Christie" <[EMAIL PROTECTED]> > > >>>To: "NZ Borland Developers Group - Delphi List" > <[EMAIL PROTECTED]> > > >>>Sent: Thursday, August 05, 2004 1:36 PM > > >>>Subject: Re: [DUG] Welcome back problem > > >>> > > >>> > > >>> > > >>>>There are 3 possible arrangements > > >>>> > > >>>>A: G G C > > >>>>B: G C G > > >>>>C: C G G > > >>>> > > >>>>if we assume that we choose door number 1 each time > > >>>> > > >>>>in both A & B we have choosen incorrectly and switching > > >>> > > >>>will give us > > >>> > > >>>>the correct answer (presuming the presenter always > reveals a goat) > > >>>> > > >>>>In C we have choosen correctly and if we switch we loose. > > >>>> > > >>>>So 2 out of 3 times if we switch we win, so I think > > >>> > > >>>switching is our > > >>> > > >>>>best bet. > > >>>> > > >>>>Alister > > >>>>_______________________________________________ > > >>>>Delphi mailing list > > >>>>[EMAIL PROTECTED] http://ns3.123.co.nz/mailman/listinfo/delphi > >>>> > >>>> > >>> > >>>_______________________________________________ > >>>Delphi mailing list > >>>[EMAIL PROTECTED] > >>>http://ns3.123.co.nz/mailman/listinfo/delphi > >>> > >> > >>_______________________________________________ > >>Delphi mailing list > >>[EMAIL PROTECTED] > >>http://ns3.123.co.nz/mailman/listinfo/delphi > >> > >> > > > > > > _______________________________________________ > > Delphi mailing list > > [EMAIL PROTECTED] > > http://ns3.123.co.nz/mailman/listinfo/delphi > > > > > _______________________________________________ > Delphi mailing list > [EMAIL PROTECTED] > http://ns3.123.co.nz/mailman/listinfo/delphi > _______________________________________________ Delphi mailing list [EMAIL PROTECTED] http://ns3.123.co.nz/mailman/listinfo/delphi Visit us online at http://www.ecan.govt.nz ********************************************************************** This email and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. 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