41. The Monty Hall Problem 6. The monty hall problem. Statement of the Problem. The monty hall probleminvolves Modeling the monty hall problem. When we begin to think http://www.ds.unifi.it/VL/VL_EN/games/games6.html

Virtual Laboratories Games of Chance 6. The Monty Hall Problem Statement of the Problem The Monty Hall problem involves a classical game show situation and is named after Monty Hall , the long-time host of the the TV game show Let's Make a Deal . There are three doors labeled 1, 2, and 3. A car is behind one of the doors, while goats are behind the other two: The rules are as follows: The player selects a door. The host selects a different door and opens it. The host gives the player the option of switching from her original choice to the remaining closed door. The door finally selected by the player is opened and she either wins or loses. The Monty Hall problem became the subject of intense controversy because of several articles by Marilyn Vos Savant in the Ask Marilyn column of Parade magazine, a popular Sunday newspaper supplement. The controversy began when a reader posed the problem in the following way: Marilyn's response was that the contestant should switch doors, claiming that there is a 1/3 chance that the car is behind door 1, while there is a 2/3 chance that the car is behind door 2. In two follow-up columns, Marilyn printed a number of responses, some from academics, most of whom claimed in angry or sarcastic tones that she was wrong and that there are equal chances that the car is behind doors 1 or 2. Marilyn stood by her original answer and offered additional, but non-mathematical, arguments. 1. Think about the problem. Do you agree with Marilyn or with her critics, or do you think that neither solution is correct?

42. Critical Thinking: The Monty Hall Problem IPC Critical Thinking Workshop monty hall problem. The monty hall problem.You're on a TV game show. In front of you are three doors http://www.geocities.com/inkwire/workshop/intro/montyh3.htm

IPC C ritical T hinking W orkshop Monty Hall Problem The Problem One Question Three Answers Twenty Five ... Computer Demo The Monty Hall Problem You're on a TV game show. In front of you are three doors: there's a great prize behind one door, and nothing behind the other two. You choose a door. Then the host (Monty Hall) opens one of the two doors you didn't choose to show that there is nothing behind that door. It would be bad for the TV ratings if he opened the prize door: you'd know you had lost and the game would be over; so Monty knows where the prize is, and he always opens a door that doesn't have a prize behind it (Monty is Canadian, so you know you can trust him). You're now facing two unopened doors, the one you originally picked and the other one, and the host gives you a chance to change your mind: do you want to stick with the door you originally chose, or do you want to switch to what's behind the other door? The Question What should you do to have the best chance of winning? The Answers There are only three answers: a) stick with the door you originally chose

43. The Monty Hall Problem: The Answer The monty hall problem The Answer. You should take the host up onhis offer to switch doors. (Most people think either that you http://www.geocities.com/Athens/Olympus/2178/answer.html

The Monty Hall Problem: The Answer You should take the host up on his offer to switch doors. (Most people think either that you shouldn’t switch or else that it doesn’t matter.) By switching, you double your chance of getting the car. When you make your initial pick of one of the three doors, you have a 1 in 3 chance of being right. That means that there’s a 2 in 3 chance that the car is somewhere else. When the host shows you a door with a goat behind it, that doesn’t change the chance that you were right on your initial pick. (Since there are two goats, he can always find a door with a goat behind it that you haven’t picked.) You still only have a 1 in 3 chance of having been right. The bit of information he’s given you only tells you that there’s no chance the car is behind that door. Since there’s a 2 in 3 chance that the car is somewhere other than behind the door you picked, switching doors increases your chance of getting the car from 1 in 3 to 2 in 3. [After posting that on a mailing list, I got this reply. Following is (part of) my answer.] Bill wrote: It’s been years

44. Quantum Information: Quantum Monty Hall The monty hall problem is a wellknown problem in statistics, which time andagain leads to controversies because of its counter-intuitive solution. http://www.imaph.tu-bs.de/qi/monty/

IMaPh Research Areas Quantum Information Monty Hall Simulation The Quantum Monty Hall Problem The Monty Hall problem is a well-known problem in statistics, which time and again leads to controversies because of its counter-intuitive solution . Here we consider a quantum version, which illustrates nicely some differences between classical and quantum information . As in the classical case a simulation helps to understand the solution. You will find on this site: An explanation of the quantum version of the problem, in parallel with a description of the classical version. Here we assume familiarity with basic quantum mechanics. A Simulation of the quantum version, in the form of a Java applet with instructions and some hints on what experiments you might try. A paper explaining the theory of the problem. A reminder of the solution of the classical problem , with links and references. A description of an even more quantum version, in which the prior information of the show master is encoded in an entangled state. The game Classical Quantum The basic setting of the problem is a game show. There is a prize hidden behind one of three doors, which the player (called P here) can get, if he opens the correct door. His opponent is the host of the show (called Q for quiz master), who basically tries to confuse the player.

45. Sci.math FAQ: The Monty Hall Problem Subject sci.math FAQ The monty hall problem. This article was archivedaround 17 Feb 2000 225551 GMT All FAQs in Directory sci http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/montehall.html

Note from archivist@cs.uu.nl : This page is part of a big collection of Usenet postings, archived here for your convenience. For matters concerning the content of this page , please contact its author(s); use the source , if all else fails. For matters concerning the archive as a whole, please refer to the archive description or contact the archivist. Subject: sci.math FAQ: The Monty Hall Problem This article was archived around: 17 Feb 2000 22:55:51 GMT All FAQs in Directory: sci-math-faq All FAQs posted in: sci.math Source: Usenet Version Archive-name: sci-math-faq/montehall Last-modified: February 20, 1998 Version: 7.5 http://www.cs.unb.ca/~alopez-o Assistant Professor Faculty of Computer Science University of New Brunswick

46. 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)=_

47. Monty Hall CONCLUSION As for the correct solution to the monty hall problem, it reallydepends on one's interpretation of the way the game show is run. http://barryispuzzled.com/zmonty.htm

48. The Monty Hall Problem Home July 1997 - monty hall problem. The monty hall problem. MontyHall This has come to be known as the monty hall problem. It is http://www.visi.com/~sgrantz/july/monty.html

Home July 1997 -> Monty Hall Problem The Monty Hall Problem Monty Hall hosted a game show around 25 years ago in which he fast-talked people into making deals for cash and prizes. Audience members wore ridiculous costumes, and at the end of the show, Monty would wander through the melange of clowns, chickens, and chefs, offering quick cash if selected people could produce a desired item. "I'll give you $40 if you have hairspray in your purse," Monty would ask some woman in a green bodysuit with foam flower petals surrounding her head. It was a laugh riot. The centerpiece of the show, however, was "The Deal". Monty would pick someone from the audience, give them cash, the tell them that behind one of three doors was a lovely gift. They could keep the cash, or pick one of the doors. After picking, say, door #1, the real fun began. Without opening door #1, Monty would reveal the contents of door two, usually a lovely Amana kitchen appliance. Then he would ask if they wanted to switch from door #1, contents unknown, to the remaining door, #3. This has come to be known as the Monty Hall Problem. It is very well known in mathematical and statistical circles because the correct answer to the problem is counterintuitive. You should always switch.

49. 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.

50. Harry's Monty Hall Page The monty hall problem is one that comes up fairly regularly in alt.folklore.urban,and it is one that people consistently have problems understanding, hence http://www.het3.com/monty-main.html

Harry's Monty Hall Page The Monty Hall Problem is one that comes up fairly regularly in alt.folklore.urban, and it is one that people consistently have problems understanding, hence it is only reasonable to have a sort of FAQ for it. This FAQ is organized thusly: Part 1: The Monty Hall Problem itself, and the Answer Part 2: Compelling Explanations of the Answer Part 3: Common Misconstructions of the Problem, and their Rebuttals Part 1: The Monty Hall Problem, and the Answer You are a guest on Let's Make a Deal, hosted by Monty Hall. He presents you with three doors, behind one of which is a Brand! New! Car! and behind the other two are goats. You are given one guess as to which door has the car. Monty then opens one of the other doors to show you a goat, and you are given the opportunity to switch to the other unopened door. Should you switch, or should you stay with your initial guess? Note: There are certain assumptions in the problem that are important to understand. One is that Monty is honest, and always behaves the same way. This means that you are always provided the choice to switch, which is apparently not the case on the actual Let's Make a Deal show, and that Monty's subsequent behavior does not change relative to whether you initially picked the winning door. This is a problem about probability analysis, not about realistically modeling the behavior of a game show host. And the answer is... yes, you should switch. Your odds of winning increase to 2 in 3 if you switch, and remain at 1 in 3 if you do not.

51. The Monty Hall Problem http://www.liacs.nl/~jeggermo/Monty_Hall/english/

52. Monty Hall Problem Translate this page Das Monty-Hall-Problem. Mit dieser straight-forward Analyse, kommt man ebenfallsauf obige Lösung. Weiterführende Links zum monty hall problem. http://www.univie.ac.at/spareg/cc/lehrreich/stat/MontyHall/MontyHall.html

Das Monty-Hall-Problem Im Folgenden wird das sogenannte Monty Hall Problem oder Monty Hall Dilemma besprochen, auch bekannt unter dem Namen Am Ende dieser Datei habe ich noch einen und Links zu internationalen Seiten im Internet Nun aber zum Artikel: Schönheit des Denkens Eine Knacknuss aus der Wahrscheinlichkeitsrechnung entzweit die US-Nation: Wer hat recht im Streit um das "Drei-Türen-Problem?" Im Fernsehstudio steuert die Show "Let´s make a deal" ihrem Höhepunkt entgegen. Der Kandidat hat die Endrunde erreicht, und damit beginnt ein Ritual, das ihm die Chance eröffnet, ein Auto zu gewinnen Der Supergewinn verbirgt sich hinter einer von drei Holztüren; hinter den beiden anderen ist, gleichsam als lebende Niete, jeweils eine Ziege angepflockt. Der Kandidat trifft eine erste Wahl zwischen den drei Türen; beispielsweise entscheidet er sich für Tür Nummer 1. Seine Chancen, das Auto zu ergattern, stehen dabei eins zu drei. Einen weiteren Twist erfährt das Türenspiel im dritten Teil der Prozedur: Der Showmaster stellt dem Kandidaten frei, seine Wahl ("Tür 1") noch einmal zu überdenken und vielleicht die Tür 2 statt der Tür 1 zu öffnen. Soll er, oder soll er nicht? Kann der durch einen Wechsel seines Tür-Tips die Gewinnaussichten verbessern? Oder bleibt die Gewinnchance, egal auf welche der beiden Testtüren seine Wahl fällt, halbe-halbe? Diese Streitfrage beschäftigt und entzweit seit Monaten die amerikanische Nation. Sie wurde in den Unterständen der US-Soldaten am Golf wie auf den Fluren des Geheimdienstes CIA, aber auch in den amerikanischen Eliteuniversitäten mit Leidenschaft diskutiert; auch deutsche Professoren ereifern sich mittlerweile in der Hamburger Zeit über Türen, Autos und Ziegen.

53. Critical Thinking: The Monty Hall Problem CriticalThinking monty hall problem The monty hall problem. You'reon a TV game show. In front of you are three doors there's a http://www.univie.ac.at/spareg/cc/lehrreich/stat/MontyHall/montyh3.htm

C ritical T hinking Monty Hall Problem The Problem One Question Three Answers Eighteen ... Arguments The Monty Hall Problem You're on a TV game show. In front of you are three doors: there's a great prize behind one door, and nothing behind the other two. You choose a door. Then the host (Monty Hall) opens one of the two doors you didn't choose to show that there is nothing behind that door. It would be bad for the TV ratings if he opened the prize door: you'd know you had lost and the game would be over; so Monty knows where the prize is, and he always opens a door that doesn't have a prize behind it (Monty is Canadian, so you know you can trust him). You're now facing two unopened doors, the one you originally picked and the other one, and the host gives you a chance to change your mind: do you want to stick with the door you originally chose, or do you want to switch to what's behind the other door? The Question What should you do? The Answers There are only three answers: a) stick with the door you originally chose b) switch to the other door, or

54. Intelligent Software - The Monty Hall Problem The monty hall problem. The monty hall problem is a fun little probability problem.Monty Hall, the host of a game show, presents three doors to you. http://qed.newcastle.edu.au/intelligent/monty/

55. Harvard University Press/Features/Randomness/Monty Hall order RANDOMNESS, The monty hall problem Suppose a reader. The problemis named after the host of Let's Make a Deal, Monty Hall. 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

56. The Monty Hall Problem http://www.statslab.cam.ac.uk/~steve/Teaching/Monty/Monty.html

57. Monty Hall Worksheet Monty Hall Worksheet This worksheet will take you through the Webpages looking at the monty hall problem. To start off, you'll http://www.statslab.cam.ac.uk/~steve/Teaching/Monty/

Monty Hall Worksheet This worksheet will take you through the Web pages looking at the Monty Hall problem. To start off, you'll need to print out this page, and then follow the instructions below. Getting Started Begin by setting your Web Browser to point at the following URL: http://www.statslab.cam.ac.uk/~steve/Teaching/Monty/Monty.html Introduction The first page introduces the Monty Hall puzzle, in which you are asked to decide between two different strategies for winning the star prize on a game show. You are asked to guess which strategy (if either) you think is the best. Write your answer below. Write down what you think your chances are of winning the star prize under the two different strategies. Discuss the problem with the class. Do you all agree? Practical 1 Follow the instructions on the screen, to simulate being the contestant on the game show. Try switching and not switching and keep a record of the number of times you win when you switch and when you don't. No of times you win No of times you lose Don't switch Switch Which is Best?

58. Mathematica Information Center: Mathematica Pearls: Monty Hall Problem , MontyHall problem (source Marilyn Vos Savant, Parade Magazine, Sept. 9, 1990),...... Title, Downloads, Mathematica Pearls monty hall problem, Author, http://library.wolfram.com/database/Articles/1632/

All Collections Articles Books Conference Proceedings Courseware Demos MathSource: Packages and Programs Technical Notes Title Mathematica Pearls: Monty Hall Problem Author Donald Piele Journal / Anthology Mathematica in Education and Research Year: Volume: Issue: Page range: Description Monty Hall problem (source - Marilyn Vos Savant, Parade Magazine, Sept. 9, 1990) Subjects Mathematics Probability and Statistics Mathematics Recreational Mathematics Downloads Files specific to Mathematica 2.2 version: Monty.ma (12.8 KB) - Mathematica Notebook 2.2 or older

59. DNKB: The Monty Hall Problem Wanna know more, you'll just have to email Dave or Kim. Copyright © 19972003David E. Burke Powered by Moveable Type The monty hall problem http://dnkb.com/coreblog/archives/000109.shtml

@import "/style_core2.css"; Rehoboth Beach, Delaware Updated every minute! Nothing right now. Where the Suckers Moon: The Life and Death of an Advertising Campaign. Learn about the secret lives of agency creatives and account managers, and watch them knock heads with a major-brand client! Well, there's the whole career thing. There's updating this web site . And there's reading other web sites. Wanna know more, you'll just have to email Dave or Kim. Opinions on this site are those of the authors. They are not (unless coincidentally) the opinions our employers, or anyone else. The Monty Hall Problem I was talking with a buddy this afternoon, and the subject of the Monty Hall Problem came up. Have you heard of this? It's without a doubt the most confounding mathematical phenomenon I've ever encountered (though really not much competition there.) So here it is: A la Let's Make A Deal , you're given three doors to pick from. Behind one of the doors, a new $50 million yacht. Behind the other two doors, Rice-A-Roni and a candy bar. Let's say you choose Door Number One. Okay, now Monty Hall (or Pat Sajak or whoever) reveals that behind Door Number Two is the Rice-A-Roni.

60. Das Ziegenproblem / Monty Hall Problem Translate this page Das Ziegenproblem / monty hall problem. Veith Tiemann. Juli 1998. Beschreibung. Aboutthis document Das Ziegenproblem / monty hall problem http://www.wiwi.uni-bielefeld.de/StatCompSci/lehre/material_allgemein/ziegen/zie

Das Ziegenproblem / Monty Hall problem Veith Tiemann Juli 1998 Beschreibung Das Ziegenproblem Wechseln! Wahrscheinlichkeitsrechnung und Emotionen Aber auch die reale Situation in der Spielshow Let's make a deal Der Moderator benutzt sein Wissen und macht suggestive Gesten und Bemerkungen zum Kandidaten wechseln all denen geben, die das Auto gewinnen wollen. Es lohnt sich also zu wechseln. Wir verbessern unsere Trefferwahrscheinlichkeit immerhin um den Faktor zwei von 1/3 auf 2/3. Marylin vos Savant ist die Autorin der Kolumne Ask Marylin im Parade Magazine . Dort hatte sie im September 1990 die Aufgabe, auf die hier diskutierte Fragestellung zu antworten, nachdem ein Leser sie gestellt hatte. Ihre Antwort kennen wir. Das gleiche Magazin druckte im Dezember die dem genau entgegengesetzten Meinungen von drei akademisch titulierten ( Ph.D's ) Lesern ab. Frau vos Savant verteidigte ihre Behauptung bis zur Febrauar-Ausgabe. Von da an schien sich die halbe Welt der Sache annehmen zu wollen. Tausende von Briefen New York Times schaffte, zumal das Problem ja nun nicht mit jener Leserfrage vom statistischen Himmel fiel, sondern im Gegenteil, die Problematik unter anderen Namen bekannt war. Mosteller beschreibt zum Beispiel das

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