61. The Monty Hall Problem the monty hall problem, indepth solution. In order to prove the answer to the MontyHall Problem, we need to learn a little bit about conditional probability. http://www.andrew.cmu.edu/user/nal/monty_sol2.htm

the monty hall problem, in-depth solution In order to prove the answer to the Monty Hall Problem, we need to learn a little bit about conditional probability. This field of mathematics deals with determining the probability of one event once another related event has already happened. The notation used is p(A/B), meaning the probability of event A happening once B has happened. This is useful, but what if you only know p(B/A)? We can use Bayes’ Theorem, which states p(A/B) x p(B) = p(B/A) x p(A). To prove Bayes’ Theorem, imagine a bag containing 3 blue marbles and 5 red marbles. We will pick 2 without replacing them. The probability of picking a blue marble is 3/8. Once this has happened, the probability of picking a red marble, p(R/B), is 5/7, since there are only 7 marbles left. So, p(R/B) x p(B) = 5/7 x 3/8 = 15/56. Now, imagine that we pick a red marble first; the chance of doing so is 5/8. After this, the probability of picking a blue marble, or p(B/R), is 3/7. Thus, p(B/R) x p(R) = 3/7 x 5/8 = 15/56. Note that the results of these two paths are the same, proving the usefulness of Bayes’ Theorem.

62. Monty Hall Problem Definition Meaning Information Explanation kottke.org Comment on The monty hall problem17 comments on The monty hall problem . gogol13 http//everything2.com/?node_id=1532241http//www.qubit.org/library/intros/gmn/gmn.html bing This guy s http://www.free-definition.com/Monty-Hall-problem.html

A B C D ... Contact Beta 0.71 powered by: akademie.de PHP PostgreSQL Google News about your search term Monty Hall problem This article has been nominated on . Please refer to that page if you wish to second or contest the nomination. The Monty Hall problem is a puzzle in probability that is loosely based on the American game show Let's Make a Deal ; the name comes from the show's host Monty Hall . In this puzzle a contestant is shown three closed doors; behind one is a car, and behind each of the others is a goat. The contestant chooses one door and will be allowed to keep what is behind it. Before the door is opened, however, the host opens one of the other doors and shows that there is a goat behind it. Should the contestant stick with the original choice or change to the remaining door; or does it make no difference? The question has generated heated debate. As the standard answer appears to contradict elementary ideas of probability, it may be regarded as a paradox . As the answer relies on assumptions that are not in the statement of the puzzle and are not obvious, it may also be considered a trick question. Inhaltsverzeichnis 1 Problem and solution 1.1 The problem

63. A Simulation Of The Monty Hall Problem A simulation of the monty hall problem. The monty hall problem can bestated as follows A gameshow host displays three closed doors. http://www.ram.org/computing/monty_hall/monty_hall.html

A simulation of the Monty Hall problem The Monty Hall problem can be stated as follows: A gameshow host displays three closed doors. Behind one of the doors is a car. The other two doors have goats behind them. You are then asked to choose a door. After you have made your choice, one of the remaining two doors is then opened by the host (who knows what's behind the doors), revealing a goat. Will switching your initial guess to the remaining door increase your chances of guessing the door with the car? The answer is yes. I did a simulation of this problem in the following manner: Randomly assign the car to be behind one of the three doors. The other two doors will be assigned goats. Randomly pick one of the three doors. Open one of the two remaining doors to reveal a goat: if the choice in (2) was the one behind which the car was hidden, then randomly choose between the remaining two doors. if the choice in (2) was not the one behind which the car was hidden, then one of the two remaining doors contains a car and the other contains a goat. The one with the goat is always chosen. Pick whether to switch or stay with the choice made in (2) randomly.

64. Andrewgraham.co.uk.games: The Monty Hall Problem the monty hall problem. The true result, however, is quite easy to verify. I ve writtena simulation of the monty hall problem in Flash to try out for yourself. http://www.andrewgraham.co.uk/monty.html

the monty hall problem It's hard to believe, isn't it? After all, when the host opens one door there's a straight choice between two doors - one hiding a goat, the other the car. The argument that there's a fifty-fifty chance of winning is a very seductive one - but it's wrong. The problem is based on a real-life scenario from the American TV gameshow Let's Make a Deal and gets its name from the show's host. The problem gained notoriety when it became the subject of the syndicated American newspaper column Ask Marilyn . Responding to a correspondent who posed the problem, Marilyn vos Savant provided a detailed explanation of the correct answer, explaining that there is a two in three chance of winning the car by switching doors. The outcome is so different from our intuition that it is very hard to accept. Indeed, after her first explanation Marilyn received a vociferous postbag from a disbelieving public. Many letters came from indignant mathematicians who failed to agree with vos Savant. The true result, however, is quite easy to verify. I've written a simulation of the Monty Hall Problem in Flash to try out for yourself.

65. Not The Monty Hall Problem Not The monty hall problem. This is what people who get the MontyHallProblemwrong think the MontyHallProblem is. There are three http://c2.com/cgi/wiki?NotTheMontyHallProblem

66. John's Jottings: The Monty Hall Problem John s Jottings. Home » Archives » The monty hall problem. July 14, 2003.The monty hall problem. Posted by john at 0953 PM Thoughts (2). http://www.johnsjottings.com/archives/2003/07/14/the_monty_hall_problem.html

Home Archives July 14, 2003 The Monty Hall Problem Posted by john at 09:53 PM Thoughts (2) I haven't seen the Monty Hall Problem mentioned for some time until it was recently brought up in rec.gambling.craps. I was all set to write up a little something on it until a Feedster search quickly discovered that it has been discussed at length recently, with active participation by commenters, by Brad Wilson (The .Net Guy) in The Let's Make a Deal Paradox and I won't go over that ground again, except to point his article out and provide a few more links. The premise behind the Monty Hall problem is this: Given the choice of 3 doors you select one behind which exists a prize. After selecting the door you are shown the contents of another door, which does not contain the prize you seek. The question is should you switch to the last remaining door or keep your initial selection? Intuition would say it is a 50/50 shot so no advantage to switching, but intuition would be wrong. This problem has tricked many a mathematician. Just ask Marilyn vos Savant, who started this whole mess by answering this question correctly (that you should switch) in a Parade Magazine article over a dozen years ago. Here is a pretty good summary of how that went. It looks like it took Marilyn a few different articles to convince the naysayers. Interestingly enough there are clear parallels between what Marilyn went through and some of the comments from Brad's article. Some people just can't suspend belief in their intuition!

67. The Monty Hall Problem HomeThe monty hall problem in Bridge. THE MONTY HALL TRAP BY PHILMARTIN Behind one of these three doors, shouts Monty Hall, is http://www.himbuv.com/experteng.html

The Monty Hall Problem in Bridge THE MONTY HALL TRAP BY PHIL MARTIN "Behind one of these three doors," shouts Monty Hall, "is the grand prize, worth one hundred thousand dollars! It's all yours if you pick the right door." "I'll take door number one," you say. "Let's see what's behind door number - No! Wait a minute!" says Monty Hall. "Before we look, I'll offer you twenty thousand dollars, sight unseen, for whatever's behind door number one." "No! No!" shouts the audience. "Of course not," you say. "Even assuming the booby prizes are worth nothing, the expected value of my choice is thirty three and a third thousand dollars. Why should I take twenty thousand?" "All right," says Monty Hall. "But before we see what you've won, let's take a look behind door number two!" Door number two opens to reveal one of the booby prizes: a date in the National Open Pairs with Phil Martin. You and the audience breathe a sign of relief. "I'll give you one last chance," says Monty Hall. "You can have forty thousand dollars for what's behind door number one."

68. The Monty Hall Problem The monty hall problem. Marilyn gives the correct solution to a simplebut tricky problem. She is viciously attacked by an army of http://www25.brinkster.com/ranmath/marlright/monty.htm

var google_language="en"; var adHB=true; wDoL("top","KKUPHDA"); wCls("KKUPHDA"); wDoL("btm","KKUPHDA"); showA("KKUPHDA"); The Monty Hall Problem Marilyn gives the correct solution to a simple but tricky problem. She is viciously attacked by an army of highly-placed academics who insist that she is wrong. She holds her ground. They finally admit their error and are repentant. Monty Hall is the MC of a television quiz show called Let's Make A Deal. One of the games he offers uses three doors. Behind one door is an expensive automobile and behind each of the others is a goat. Nobody but Monty and the stage crew know which door leads to the automobile. The essence of the game is that the contestant is permitted to choose one of the three doors. If he chooses the right door he wins the automobile. If he chooses a wrong one he gets goat cheese. There is a twist. After the contestant has chosen a door Monty asks him if he wants to change his mind. To help him, or perhaps to confuse him, he opens one of the doors not chosen and shows that it conceals one of the goats. The question is, should you stick with the door you chose originally or should you accept the switch offered by Monty, and what is the probability of winning the automobile in each case? There has been some discussion about whether or not Monty always offered the switch and if his doing so depended on whether the contestant chose the right door to begin with. Monty said that he did not always offer the switch. Sometimes he would offer it to lure the contestant away from the right door, and to keep the audience off balance sometimes he would bluff and offer the switch when the contestant had chosen wrongly to see if he could make him be stubborn. If we knew the probability that Monty would offer the switch as a function of the accuracy of the contestant's choice we could use it in deciding the best strategy. That is the approach we would take in attempting to crack the game commercially. In presenting it as a puzzle, however, it is customary to assume that Monty always offers the switch regardless. Decide on your strategy and turn the page when you are ready.

69. The Monty Hall Problem, Part 2 The monty hall problem, Part 2. We problems. If you have an axe to grindtry a newsgroup such as rec.puzzles. monty hall problem Links. http://www25.brinkster.com/ranmath/marlright/monty1.htm

var google_language="en"; var adHB=true; wDoL("top","KKUPHDA"); wCls("KKUPHDA"); wDoL("btm","KKUPHDA"); showA("KKUPHDA"); The Monty Hall Problem, Part 2 We are proceeding on the basis that you have no advance knowledge of which door the automobile is behind and that Monty offers the switch whether you have chosen the correct door or not. The popular but incorrect answer is that the probability of winning is 1/2 whether you switch or not. The correct answer is that you should always switch and if you do your probability of winning is 2/3. That is the answer Marilyn gave, and it inspired a flood of indignant mail telling her that she was wrong. Here is the way Monty explains it. When the contestant made his first choice his probability of being right was 1/3. When Monty opened the second door the contestant would think his chance of being right had gone up to 1/2. It hadn't, though, it was still 1/3; and since the only other place the auto could be was behind the third door, the probability of it's being there was 2/3. This is the way Marilyn first explained it: "Suppose there were 100 doors and Monty opened 98 of them. You'd switch pretty fast then, wouldn't you?"

70. The Monty Hall Problem This Is Broken (rss); Weblogs at ILG.com (rss). The monty hall problem.Brad Wilson posted aC demonstration of the classic monty hall problem. http://www.peterprovost.org/archive/2003/06/10/545.aspx

Geek Noise Peter Provost's look into the world of technology, Microsoft .NET, and other fun stuff... Quick Links Home Contact Me RSS 2.0 Feed ATOM Feed ... Login Suggested Reading Post Categories Books, Music, TV and Movies (rss) Community (rss) ... (rss) Article Categories Personal Security and Networking Software Development Image Galleries 2004 Landscaping Project Archives June, 2004 (4) May, 2004 (57) April, 2004 (15) March, 2004 (19) ... February, 2003 (64) Logos and Stuff Blog Stats Posts - 859 Stories - 6 Comments - 292 Trackbacks - 25 Communities Denver Pragmatic Practitioners Denver Visual Studio .NET User Group Northern Colorado .NET SIG South Colorado .NET User Group Events TechEd 2004 WIN-DEV 2004 Open Source Projects CruiseControl.NET (rss) NAnt (rss) ... WebSVN Popular Posts HOWTO: Adopt .NET For Free! Test-Driven Development in .NET Recommended Links .NET Remoting FAQ Scott's Ultimate Tools List Tips for a Successful Microsoft Presentation Sites I Own Provost Family Site Virtual PC FAQ Zundapp Bella Information Center Weblogs I Read .NET Developers (rss) Andy Hunt (rss) ... posted a C# demonstration of the classic Monty Hall Problem . I remember getting into a huge argument with some of my co-workers at a previous job and I basically did the same thing. I sat down and busted out a quick program that played the game. I think it was in VB3 though... :) The most interesting thing is to see people in Brad's comments arguing that this isn't real. That it is a hoax or something. It isn't. It worked EVERY TIME. Probabilities don't lie.

71. Three Door Or Monty Hall Problem QA 233 (Basic Business Statistics). The Three Door Problem (or MontyHall Problem). Suppose you are presented with three closed doors. http://www.cab.latech.edu/public/fac-staff/Homes/Jcochran/qa233/three door probl

QA 233 (Basic Business Statistics) The Three Door Problem (or Monty Hall Problem) Suppose you are presented with three closed doors. Behind one of these doors is a large cash prize, and behind the other two doors are old, smelly goats. The host of this game (Monty Hall) knows which door hides the prize, and he invites you to choose a door (1, 2, or 3). After you announce your selection, Monty will open one of the remaining doors to reveal a goat. He then offers you a chance to switch from the door you originally chose to the remaining closed door. Should you accept the offer to switch doors? Why or why not? Return to the QA 233 Virtual Classroom

72. The Monty Hall Problem The monty hall problem. This problem is based on the game show, Let sMake A Deal , which starred Monty Hall. There was much discussion http://faculty.gvsu.edu/aboufade/web/monty.htm

The Monty Hall Problem This problem is based on the game show, "Let's Make A Deal", which starred Monty Hall. There was much discussion of this problem in 1990 and 1991 in the column "Ask Marilyn" in Parade Magazine . Here is the problem: Suppose that you are on a game show, and you're given the choice of three doors. Behind one door is a car; behind the others, goats. You pick a door, say No.1, and the host, who knows what's behind the other doors, open another door, say No. 3, which has a goat. He then says to you, "Do you want to switch and pick door #2?" Is it to your advantage to switch? We will study this problem using probability. Trial Contestant Chooses: You Show Goat Under: Then Contestant Chooses: Did Contestant Switch? Did Contestant Win or Lose? Number of switch and win Number of switch and lose Number of stay and win Number of stay and lose P(winning) = P(losing)=_

73. Monty Hall Problem - Wikipedia, The Free Encyclopedia PhatNav s Encyclopedia A Wikipedia . monty hall problem. See Empirical proofof the monty hall problem for a Perl program which demonstrates the result. http://www.phatnav.com/wiki/wiki.phtml?title=Monty_Hall_problem

74. RateMyProfessors.com Forums General Monty Hall Problem Home General monty hall problem, Not logged in. Login or create an account. MontyHall Problem posted by DrWolfy, Please login to reply to this message. http://www.ratemyprofessors.com/jive/vodka/viewThread.jsp?forum=2&thread=4126

75. Zeal.com - United States - New - Entertainment - Games - Puzzles - Math Puzzles A great resource for United States New - Entertainment - Games - Puzzles -Math Puzzles - monty hall problem. monty hall problem Preview Category, http://zeal.com/category/preview.jhtml?cid=10159400

76. Answers To Technical Interview Questions Tuesday, March 13, 2001 monty hall problem aha! another well known problemin probability is the monty hall problem. you are presented http://www.techinterview.org/Puzzles/fog0000000045.html

techInterview Answers to technical interview questions - accepting donations for dogs home faq reading ... petfinder *new* techInterview bible thank your brain save a dog's life Tuesday, March 13, 2001 monty hall problem aha another well known problem in probability is the monty hall problem. you are presented with three doors (door 1, door 2, door 3). one door has a million dollars behind it. the other two have goats behind them. you do not know ahead of time what is behind any of the doors. monty asks you to choose a door. you pick one of the doors and announce it. monty then counters by showing you one of the doors with a goat behind it and asks you if you would like to keep the door you chose, or switch to the other unknown door. should you switch? if so, why? what is the probability if you don't switch? what is the probability if you do. lots of people have heard this problem.. so just knowing what to do isn't sufficient. its the explanation that counts! solution: monty hall home software development bug tracking software ... Software Quality

77. Harvard University Press/Features/Randomness/Monty Hall RANDOMNESS, The monty hall problem Suppose reader. The problem is named afterthe host of Let s Make a Deal, Monty Hall. Return to BRAINTEASERS. http://www.hup.harvard.edu/features/benran/montyhall.html

The Monty Hall Problem Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Do you keep door No. 1 or do you make the switch to door No. 2? pages 180-181, Randomness 1. This now infamous problem was originally appeared in the September 1990 Parade column, "Ask Marilyn," where Marilyn vos Savant was asked the question by a reader. The problem is named after the host of Let's Make a Deal, Monty Hall. Return to BRAINTEASERS

78. The Monty Hall Problem The monty hall problem. Standards of rationality are As an example,are you familiar with the monty hall problem? Imagine you’re a http://personal.bgsu.edu/~roberth/monty.html

The Monty Hall Problem Standards of rationality are a lot more complicated than a handful of truisms like “don’t contradict yourself.” There are questions of what counts as evidence, how much and what quality of evidence is needed to establish a claim, or make it reasonable to believe or to overturn a contrary belief, how much weight should be accorded to testimony, how beliefs should be updated on the basis of new evidence and argument, what principles of reasoning should be accepted, and lots more. One area where the problem shows up is in reasoning about probabilities. Most people are pretty bad at it. (There’s a vast literature in psychology about evidence of human irrationality in dealing with probabilities.) And it’s not just that they make mistakes or are careless. If that were the explanation, you’d expect a random distribution around the correct answers. Instead, the answers people give are systematically biased. We come to the same wrong conclusions – which is to say we’re operating with mistaken principles of probabilistic reasoning. People who (eventually) get to be good at probabilistic reasoning generally have to go through a process of beating their intuitions into submission. As an example, are you familiar with the Monty Hall Problem? Imagine you’re a guest on a game show like “Let’s Make a Deal.” The host is about to offer you a choice of three doors behind which prizes may be. Once he hears your answer, but before he opens the door you’ve chosen, he’s going to give you an additional piece of information and ask if you want to change your selection. He will do this regardless of what you choose, and there are no tricks like sliding platforms behind the doors to shift the prizes around.

79. The Monty Hall Problem The monty hall problem. Which door do you choose and why? . Jarno. Responses to thismessages Re The monty hall problem Osiris 151834 01/23/01 (0) responses http://users.cgiforme.com/fbendz/messages/163.html

The Monty Hall problem Post a new reply Back to the message board This message was posted by Jarno , posted on September 28, 2000 at 09:46:36 coming from Mood of this message: If you haven't encountered this before, you are in for a major brain twister... or a major headache... Here's the problem: "You are a game show contestant who must choose to open one of three doorsA, B or C. Behind two lies a banana, behind the third, $10,000. You win what is behind your chosen door. You pick a door, A, but before you open it, Monty (the host, who knows what is behind each door) opens one of the two remaining doors (C) to reveal a banana. He offers you the chance to change your choice from A to B, providing you pay him $10. Which door do you choose and why?" -Jarno Responses to this messages: Re: The Monty Hall problem Osiris 0) responses The other one! Fredrik Bendz 2) responses Re: The other one! Jarno 1) response Re: The other one! Eric 0) responses Re: The Monty Hall problem cfm 0) responses Re: The Monty Hall problem Simon Goldring 4) responses *** Spoiler - read this only if you are ready to give up!

80. Re: The Monty Hall Problem Re The monty hall problem. http://users.cgiforme.com/fbendz/messages/175.html

Re: The Monty Hall problem Post a new reply Back to the message board This message was posted by Jarno , posted on September 28, 2000 at 18:49:41 coming from This message is a reply to Re: The Monty Hall problem posted from Simon Goldring posted at September 28, 2000 at 16:25:19 ****** I am re-posting the post that I started a new thread for now that the "problem" is solved - please reply hear, and not in the new thread ****** You said: " My answer would of course be that I would stay with my original answer, A, because there would be nothing to be gained (and $10 to potentially lose) by switching my answer to B." Here's my reply: Heh! This is what everybody says (including me) at first, but the correct answer is that you substantially increase your chances at getting the price if you pay to swithch.... I know, this is extremely counter-intuitive, which is why even professional mathematicians have fallen for this one. (So don't worry, you're in good crowd) When I encountered this first I came to the same conlusion that you did (I thought it was obvious), and obstinately argued, using all sorts of seemingly good arguments why switching could not possibly increase your chances at winning. I don't want to give it all away yet, but I'll give you this much:

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