Billy Pang
tuxedo_man at hotmail.com
Fri Aug 26 01:44:24 CDT 2005
just rereading below, maybe c) should be split into two scenarios (one for catfish and another for pickerel); therefore, chances of winning would be 2/4 instead of 2/3. >From: "Billy Pang" <tuxedo_man at hotmail.com> >Reply-To: Discussion of Hardware and Software >issues<dba-tech at databaseadvisors.com> >To: dba-tech at databaseadvisors.com >Subject: Re: [dba-Tech] The Three Doors Problem >Date: Fri, 26 Aug 2005 03:27:29 +0000 > >the way it was explained to me was that if you do swap doors, you double >your chances (on paper) of winning the grand prize. this is based on the >assumption that no matter what is behind the original door you choose, the >game show host WILL ALWAYS pick out a non-winning door to tempt you to >change your mind. if you keep this assumption, given the fact that the >host will never reveal the winning door, he is telling you which door does >not have the prize and this knowledge is worked into your probability of >picking the winning door. > >that is, there are only three possible scenarios, >a) if you pick pickerel, he shows you catfish, if you swap, you win >b) if you pick catfish, he shows you pickerel, if you swap, you win >c) if you pick winning door, he shows you catfish or pickerel, if you swap, >you lose > >given this, the "swapping doors" strategy wins 2 out of 3 times. >therefore, if you don't know what is behind the door you first pick, your >best strategy is to wait for your host to give you a hint and you pick the >other door. > >Billy > >>From: Peter Brawley <peter.brawley at earthlink.net> >>Reply-To: Discussion of Hardware and Software >>issues<dba-tech at databaseadvisors.com> >>To: Discussion of Hardware and Software issues >><dba-tech at databaseadvisors.com> >>Subject: Re: [dba-Tech] The Three Doors Problem >>Date: Thu, 25 Aug 2005 22:03:18 -0500 >> >>John >> >> >And Arthur, while your door just increased from 1 in 3 to 1 in 2, so did >>the >> >other door. It matters not whether you switch or whether you stay, you >>have >> >a 50/50 chance of winning. There is no particular reason to switch, but >>you >> >don't affect your odds in the slightest by switching. Pick a door (of >>the >> >two remaining), any door, and you have a 50/50 chance. >> >>You can test your theory empirically. Visit >>http://people.hofstra.edu/staff/steven_r_costenoble/MontyHall/MontyHall.html. >>Do a dozen trials of holding your choice, and a dozen of switching it. Kep >>a count of the number of wins with each strategy. That gives you a 2x2 >>table. Now visit http://www.unc.edu/~preacher/fisher/fisher.htm, plug in >>your numbers in the little table near the bottom, and click 'Calculate'. >>The 'this tail' number is the probability that your numbers could have >>come about by chance from a scenario where the probabilities were 50-50. >> >>Or if you prefer, you can keep your theory :-) . >> >>PB >> >>----- >> >>John W. Colby wrote: >> >>>LOL, but the answer is screwy. Now take the example where TWO people are >>>choosing doors simultaneously. The third door is shown to NOT contain >>>the >>>prize. Both people should swap by the logic of the puzzle, but one of >>>them >>>is still going to lose and the other win. Each person (door) has a 50% >>>probability of winning. Which one will win? There is no way to predict >>>the >>>answer, each person has a 50% probability of winning the prize. >>> >>>The logic SOUNDS good but is screwy. Each door has a 1 in 3 chance of >>>being >>>a winner. Eliminate one door and each door has a 1 in 2 chance of being >>>a >>>winner. It matters not whether the third door is eliminated during the >>>game >>>or before the game starts. >>> >>>And Arthur, while your door just increased from 1 in 3 to 1 in 2, so did >>>the >>>other door. It matters not whether you switch or whether you stay, you >>>have >>>a 50/50 chance of winning. There is no particular reason to switch, but >>>you >>>don't affect your odds in the slightest by switching. Pick a door (of >>>the >>>two remaining), any door, and you have a 50/50 chance. >>> >>>John W. Colby >>>www.ColbyConsulting.com >>> >>>Contribute your unused CPU cycles to a good cause: >>>http://folding.stanford.edu/ >>> >>>-----Original Message----- >>>From: dba-tech-bounces at databaseadvisors.com >>>[mailto:dba-tech-bounces at databaseadvisors.com] On Behalf Of Stuart >>>McLachlan >>>Sent: Thursday, August 25, 2005 10:20 PM >>>To: Discussion of Hardware and Software issues >>>Subject: Re: [dba-Tech] The Three Doors Problem >>> >>> >>>On 25 Aug 2005 at 20:04, Arthur Fuller wrote: >>> >>> >>> >>>>I am the host of a TV program and you are the guest. This is the deal: >>>>there are 3 doors. Behind one of them is $100 million. Behind the other >>>>two are a dead catfish and a dead pickerel respectively. I invite you to >>>>select a door. You choose any one of the three: call it x I open another >>>>door, and say, Had you selected door y, you would have won a dead >>>>catfish. Now, would you like to stick with your original choice or >>>>switch to the other door? Does it matter? If not, why not? If so, why >>>>so? There is a clear answer to this problem. Who is going to be the >>>>first to come up with it? Arthur >>>> >>>> >>>> >>>> >>> >>>Ah, the good old Monty Hall puzzle. >>> >>>Strictly speaking, you need to qualify it by saying "I open another door >>>which I know contains a dead fish and show you the contents" If you >>>could open the money door by accident, it is a different situation. >>> >>>Anyhoo, the answers is: >>>Yes it matters, you should swap. >>> >>>I won't give the reason now 'cause it's a spoiler. I know some peole >>>will not agree with me and will go to great lengths to explain why I am >>>wrong :-) >>> >>> >>> >>> >>> >>> >>> >>> > > >>No virus found in this outgoing message. >>Checked by AVG Anti-Virus. >>Version: 7.0.344 / Virus Database: 267.10.15/81 - Release Date: 8/24/2005 > > >>_______________________________________________ >>dba-Tech mailing list >>dba-Tech at databaseadvisors.com >>http://databaseadvisors.com/mailman/listinfo/dba-tech >>Website: http://www.databaseadvisors.com > > >_______________________________________________ >dba-Tech mailing list >dba-Tech at databaseadvisors.com >http://databaseadvisors.com/mailman/listinfo/dba-tech >Website: http://www.databaseadvisors.com