Arthur Fuller
artful at rogers.com
Fri Aug 26 18:57:56 CDT 2005
You missed the crucial element of the problem, John. The Host knows what is behind all 3 doors, and thus NEVER removes the winning door. I attempted to make this clear in the presentation of the problem, and I obviously failed to do so. My apologies. -----Original Message----- From: dba-tech-bounces at databaseadvisors.com [mailto:dba-tech-bounces at databaseadvisors.com] On Behalf Of Scott Marcus Sent: August 26, 2005 9:56 AM To: Discussion of Hardware and Software issues Subject: RE: [dba-Tech] The Three Doors Problem John, The fact remains that when you picked the door, you had a 1/3 chance of being correct. If the host removes a door (no matter which because if the host removes the winning door your chance is 0%), the host just increased your chances to being 2/3 correct. Scott Marcus IT Programmer TSS Technologies Inc. www.tss.com -----Original Message----- From: dba-tech-bounces at databaseadvisors.com [mailto:dba-tech-bounces at databaseadvisors.com] On Behalf Of John W. Colby Sent: Friday, August 26, 2005 7:36 AM To: 'Discussion of Hardware and Software issues' Subject: RE: [dba-Tech] The Three Doors Problem And it is exactly because of the "intentionally and knowingly taking away the non-winning door" that the logic works. If the host "just picks a door" (which wasn't apparent from the original post) and the door "just happens to be not the prize", then the problem changes. By the fact that that the host had knowledge of and intentionally chose a door with no prize, the problem does change, and I understand the answer. By the way, the way you just worded it it still wouldn't make a difference. Only if you knowingly took away doors that you knew did not have a prize would your answer be correct. If you just randomly chose which doors to eliminate then the problem is back to 50/50 because in fact, you may very well have eliminated the prize as well (in fact probably did). >I open another door, and say, Had you selected door y, you would have won a dead catfish. No where does that imply that he intentionally chose a door with no prize, he just opened (picked at random) a remaining door, looked at the contents, and announced the contents of that door. Not that I would have gotten the answer anyway, but I do understand that by his using his knowledge to pick a door with no prize he affected the outcome. 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 Scott Marcus Sent: Friday, August 26, 2005 7:17 AM To: Discussion of Hardware and Software issues Subject: RE: [dba-Tech] The Three Doors Problem John, The problem with you logic is as follows... If there were 1,000,000 doors of which only 1 had the prize and I took away all doors except yours and another door, would you then switch? By your logic, your chance is 50/50. Sorry, but I will switch every time. Scott Marcus IT Programmer TSS Technologies Inc. www.tss.com -----Original Message----- From: dba-tech-bounces at databaseadvisors.com [mailto:dba-tech-bounces at databaseadvisors.com] On Behalf Of John W. Colby Sent: Thursday, August 25, 2005 10:44 PM To: 'Discussion of Hardware and Software issues' Subject: RE: [dba-Tech] The Three Doors Problem 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 :-) -- Stuart _______________________________________________ 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 _______________________________________________ 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 _______________________________________________ dba-Tech mailing list dba-Tech at databaseadvisors.com http://databaseadvisors.com/mailman/listinfo/dba-tech Website: http://www.databaseadvisors.com