21. Monty Hall Click here to listen to the interview. Among the examples we discussedwas the famous or should I say infamous - monty hall problem. http://www.maa.org/devlin/devlin_07_03.html

Search MAA Online MAA Home Devlin's Angle July-August 2003 Monty Hall A few weeks ago I did one of my occasional "Math Guy" segments on NPR's Weekend Edition. The topic that I discussed with host Scott Simon was probability. [Click here to listen to the interview.] Among the examples we discussed was the famous - or should I say infamous - Monty Hall Problem. Predictably, our discussion generated a mountain of email, both to me and to the producer, as listeners wrote to say that the answer I gave was wrong. (It wasn't.) The following week, I went back on the show to provide a further explanation. But as I knew from having written about this puzzler in newspapers and books on a number of occasions, and having used it as an example for many years in university probability classes, no amount of explanation can convince someone who has just met the problem for the first time and is sure that they are right - and hence that you are wrong - that it is in fact the other way round. Here, for the benefit of readers who have not previously encountered this puzzler, is what the fuss is all about.

22. Monte Hall, Let's Make A Deal, Problem Return to the SM230 home page. The monty hall problem. Analysis of the Monty HallProblem. It does not make a difference which door the contestant selects. http://www.usna.edu/MathDept/courses/pre97/sm230/MONTYHAL.HTM

Monty Hall (Let's Make a Deal) Problem Gary Fowler, revision date: January 22, 1996. Statement of problem and background. Analysis of problem. Simulation Red or black? Another challenging problem. Return to the SM230 home page. The Monty Hall Problem Monty Hall was the host of a game show called "Let's Make a Deal." This was a very popular show due in part to the finale. The stage was set with three doors. Behind each door was a prize. One prize was very desirable and valuable, e.g. , two week, all expense paid trip for two to Hawaii. There was a much less desirable prize, e.g. , living room furniture. The remaining prize was undesirable. The undesirable prize is traditionally called a "goat," but since this is the Naval Academy we will call it a "mule." After the contestant selected a door, another door was opened to show the prize and the contestant was given the choice between the already selected door or the other door that had not been opened. A few years ago, the popular press contained several articles debating whether the contestant should switch doors. This debate was sparked by an analysis of the given by Marilyn vos Savant in Parade Magazine in which she concluded that the contestant should switch. She received many letters objecting to her analysis and conclusion. Several of these letter were from college professors who teach statistics. The debate spread to professional journals including

23. 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.

24. The Monty Hall Problem Explained The monty hall problem. A game show host offers you the chance to choose one ofthree doors. Simulate the monty hall problem. A brief history of the problem. http://www.engin.umich.edu/soc/informs/MontyHall/

The Monty Hall Problem A game show host offers you the chance to choose one of three doors. You know that there is a nice price (a new car) behind one door, and a silly prize (historically, a goat, but conceivably a gift from a sponsor such as Rice-a-Roni) behind the other two. Once you have made your choice, the game show host opens a different door, to reveal a goat. He then offers you a choice: you may keep the first door you chose, or you may switch to the other closed door. Should you keep the first door, or switch to the other door? Simulate the Monty Hall problem. A brief history of the problem The Monty Hall problem apparently captured the public's attention when it was reported in Parade magazine, in Marily vos Savant's column. Before that, it was reportedly discussed in American Statistician in 1976, and in the Journal of the American Mathematical Society about ten years after that. An earlier version, the Three Prisoner Problem, was analyzed in 1959 by Martin Gardner in Scientific American . He called it "a wonderfully confusing little problem...in no other branch of mathematics is it so easy for experts to blunder as in probability theory." The answer...should you switch?

25. THE MONTY HALL PROBLEM (FRONT PAGE) The monty hall problem gets its name from the TV game show, Let s MakeA Deal, hosted by Monty Hall. RUN THE monty hall problem APPLET. http://members.shaw.ca/ron.blond/TLE/MONTY.APPLET.FRONTEND/

The Monty Hall Problem gets its name from the TV game show, "Let's Make A Deal," hosted by Monty Hall. The problem is stated below. There are three closed doors, behind one of which is a prize (the remaining doors contain "joke" prizes). Monty Hall, the game show host, asks you to pick one of the three doors. You pick a door (which remains unopened). Monty opens a door that has a joke prize. Monty then gives you the choice of either keeping your original choice, or switching to the remaining unopened door. QUESTION : To maximize the chances of winning a real prize, should you keep your choice or switch (or does it matter)? NOTE : This isn't really how the actual game show worked. This problem gets its name from the show, because it inspired the problem. The problem is interesting because most people believe that after Monty shows a losing door, the two remaining unopened doors (whether chosen or not) each have a fifty-fifty chance of being a winning door. One with a real prize, the other with a joke prize. Most people are surprised that this is not the case. At this time you can choose one of the links below. The applet is a simulation of this problem.

26. THE MONTY HALL PROBLEM (APPLET) SEE THE DESCRIPTION OF THE monty hall problem. SEE THE RESULT (AND PROOF OF THERESULT) OF THE monty hall problem. RETURN TO THE TLE APPLET SELECTION PAGE. http://members.shaw.ca/ron.blond/TLE/MONTY.APPLET.FRONTEND/MONTY.APPLET/

CONCEPT BY RICK SEPT HOW TO USE THIS APPLET Basic operation blue background. When all of the doors are opened, a listing of events for the current experiment are displayed in the top portion of the applet. When the mouse button is clicked, the results will be recorded in the chart and in the graph. Advanced operation feel for what is happening, and give a greater reinforcement to believing the result. Notes SEE THE DESCRIPTION OF THE MONTY HALL PROBLEM SEE THE RESULT (AND PROOF OF THE RESULT) OF THE MONTY HALL PROBLEM RETURN TO THE TLE APPLET SELECTION PAGE

27. Sci.math FAQ: Monty Hall Problem sci.math FAQ monty hall problem. There are reader questions on thistopic! Help others by sharing your knowledge. Newsgroups sci http://www.faqs.org/faqs/sci-math-faq/montyhall/

Usenet FAQs Search Web FAQs Documents ... RFC Index sci.math FAQ: Monty Hall problem There are reader questions on this topic! Help others by sharing your knowledge Newsgroups: sci.math alopez-o@neumann.uwaterloo.ca alopez-o@barrow.uwaterloo.ca Tue Apr 04 17:26:57 EDT 1995 Rate this FAQ N/A Worst Weak OK Good Great Current Top-Rated FAQs Are you an expert in this area? Share your knowledge and earn expert points by giving answers or rating people's questions and answers! This section of FAQS.ORG is not sanctioned in any way by FAQ authors or maintainers. Questions strongly related to this FAQ: If you are in a game show final. You have just one chance to win the price. So there is no... by Steve (8/5/2003) Other questions awaiting answers: 17142 questions related to other FAQs 2985 general questions 8012 answered questions Usenet FAQs Search ... RFC Index Send corrections/additions to the FAQ Maintainer: alopez-o@neumann.uwaterloo.ca Last Update June 05 2004 @ 00:23 AM

28. Faisal.com: The Monty Hall Problem colorblindness. The monty hall problem is a classic example of thenon-intuitive nature of statistics You are playing a game. In http://www.faisal.com/docs/monty.html

The Monty Hall Problem News Archive Quotes Documents ... Contact Search: Note: for the time being, this page requires a "4.0 browser" in order to display colors properly. I apologize to those of you with older browsers, and also to anyone who has trouble with the page due to red/green color-blindness. The "Monty Hall Problem" is a classic example of the non-intuitive nature of statistics: You are playing a game. In the game, there are three doors with prizes hidden behind them. One door hides a new car while the other two doors hide goats. If you pick the door with the car behind it, you win the car. You pick a door. At this point the game host opens another of the doors, revealing a goat. Now the game host offers you the opportunity to change your pick to the other door. Should you switch? Most people believe that there is no advantage to changing their pick: of the two remaining doors, one of them has the car, so they have a 50% chance of winning. In fact, this is incorrect: while 1 of the doors will have the car behind it, 2/3 of the time it will be the other door. It is generally to your advantage to switch.

29. The Monty Hall Problem 6. The monty hall problem. Statement of the Problem. The Monty Alwaysswitch; Never switch. Modeling the monty hall problem. When we http://www.math.uah.edu/statold/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 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: Suppose you're on a game show, and you're given a 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 doors, opens another door-;say No. 3-;which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice? 1. Think about the problem. Do you agree with Marilyn or with her critics, or do you think that neither solution is correct?

30. PHIL 158d - Critical Thinking: The Monty Hall Problem CriticalThinking Philosophy 158D 2000 monty hall problem, The MontyHall Problem. You re on a TV game show. In front of you are three http://qsilver.queensu.ca/~phil158d/intro/montyh3.htm

C ritical T hinking Philosophy 158D 2000 Monty Hall Problem The Problem One Question Three Answers Eighteen ... The 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? The Answers There are only three answers: a) stick with the door you originally chose b) switch to the other door, or

31. Nota Bene - The Monty Hall Problem - There Are Three Doors On Stage, Labeled A, Nota Bene The monty hall problem - There are three doors on stage,labeled A, B, and C. The monty hall problem. This rather interesting http://www.davidpbrown.co.uk/nota-bene/monty-hall-problem.html

The Monty Hall problem This rather interesting problem arises from a game show, Monty Hall is the host.. There are three doors on stage, labeled A, B, and C. Behind one of them is a pile of money; behind the other two are goats. You get to choose one of the doors and keep whatever is behind it. Let's suppose that you choose door A. Now, instead of showing you what's behind door A, Monty Hall slyly opens door B and reveals... a goat. He then offers you the option of switching to door C. Should you take it? (Assume, for the sake of argument, that you are indifferent to the charm of goats.) Counterintuitively enough, the answer is that you should switch, since a switch increases your chance of winning from one-third to two-thirds. Why? When you initially chose door A, there was a one-third chance you would win the money. Monty's crafty revelation that there's a goat behind door B gives no new information about what's behind the door you already chose you already know one of the other two doors has to conceal a goat so the likelihood that the money is behind door A remains one-third. Which means that, with door B eliminated, there is a two-thirds chance that the money is behind door C. Still not convinced? Perhaps it will help if you look at the game from Monty's perspective. For him, the game is very simple. No matter what door the contestant picks initially, his job is to reveal a goat and ask the contestant if they want to switch.

32. LookSmart - Directory - Monty Hall Problem Math Puzzle monty hall problem Math Puzzle Contains analyses of the monty hall problem,where the host offers a contestant the chance to switch doors. http://search.looksmart.com/p/browse/us1/us317914/us328800/us281829/us10159400/

@import url(/css/us/style.css); @import url(/css/us/searchResult1.css); Home IN the directory this category YOU ARE HERE Home Sciences Mathematics Math Puzzles Monty Hall Problem Math Puzzle - Contains analyses of the Monty Hall problem, where the host offers a contestant the chance to switch doors. Directory Listings About Andrew's Website - New Approach to the Monty Hall Problem Mathematician discusses the concept of "partial collapse" in relation to the famous probability problem. Ask Dr. Math - Monty Hall Logic Series of letters discusses this classic probability problem. Read about the correct answer and the reasoning behind it. CiteSeer - The Monty Hall Dilemma Revisited Offers a selection of mathematical papers analyzing the Monty Hall probability problem. Curmudgeon Teaches Statistics - Monty Hall Mathematics teacher explains how to arrive at the correct answer in this classic probability puzzle. Cut the Knot - Monty Hall Dilemma Most notable for its discussion of situations where there are more than 3 doors, this page explores the Monty Hall Problem, a classic probability problem. Engines of our Ingenuity - The Monty Hall Problem Essay describes this logic/math puzzle in layman's terms. Read about the famous dilemma.

33. Analysis Of The Monty Hall Problem Analysis of the monty hall problem. Kevin Gong. March 17th, 2003. There are numerousweb pages devoted to discussion and analysis of the monty hall problem. http://kevingong.com/Math/MontyHall.html

Kevin's Math Page Home Contact Home Research ... Contact Topics: Polyominoes Egyptian Fractions Graceful Graphs 16 Puzzle ... Block Swapping Problem search by FreeFind Polyominoes Home Kevin's Home Page Analysis of the Monty Hall Problem Kevin Gong March 17th, 2003 There are numerous web pages devoted to discussion and analysis of the Monty Hall problem. I hope to add something new and interesting to the discussion with an analysis of a more interesting problem. For those of you living in a mathematical cave, I'll briefly explain the problem and very little on the controversy. In 1991, Parade Magazine published a column "Ask Marilyn" in which Marilyn vos Savant replies to a reader's question: "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?' Is it to your advantage to take the switch?" Marilyn replied that the answer was yes, and there was a big uproar and mathematicians from across the country attacked her. I'll spare you the details. You can do a web search on that if you're interested. I'm more interested in the mathematics.

34. 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?

35. The Monty Hall Game PA B = PrA and B/PB. Analysis of the monty hall problem UsingConditional Probability. Take a typical situation in the game. http://www2.sjsu.edu/faculty/watkins/mhall.htm

The Monty Hall Game Monty Hall was the host of a television game show in which contestants were allowed to choose one of three doors. Behind each door was a prize but one prize was very good and the other two were not so good. Let us say that behind one door was a car and behind the other two were goats. After the contestant chose a door Monty Hall would reveal a goat behind one of the doors not chosen by the contestant. He would then give the contestant the opportunity to switch his or her choice. Intuition says that it shouldn't matter whether the contestant switches or not. Intuition is wrong in this case. To understand why we need to consider the concept of conditional probability. Analysis of the Monty Hall Problem Using Conditional Probability This is the probability of B; i.e., P[B]. This means that the conditional probability that the car is behind Door 3 given that the contestant has chosen Door 3 and has been shown that there is a goat behind Door 2 is only l/3. Therefore it is worthwhile to switch. This other conditional probability can be calculated either as or from the probability the car is behind Door 3 given that the contestant has chosen Door 3 and has been shown a goat behind Door 2. This latter probability is (1/3)(1/3)(1/2) so when it divided by P[B] one gets l/3.

36. The Monty Hall Problem MLI Home Creations Puzzles The monty hall problem. The monty hall problem. NextSome Explanations. MLI Home Creations Puzzles The monty hall problem. http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/

MLI Home Creations Puzzles The Monty Hall Problem The Monty Hall Problem An American game show left an unexpected legacy: many arguments, and more than a few Web pages. Some people even learned some probability theory. We'll leave out the theory here to concentrate on different ways to understand the problem's solution. The Problem The game show Let's Make A Deal , hosted by Monty Hall, ended each show the same way. There were three closed doors. Behind one was a prize, while the other two concealed booby prizes. Monty asked the contestant to choose a door. Then Monty opened one of the remaining doors, revealing a booby prize. Monty then offered the contestant the option to stay with the originally chosen door or switch to the other unopened door. The contestant received whatever was behind the chosen door. Now for the big question: is it better to stay , better to switch , or does it make no difference The Importance of Empiricism If you think it doesn't make a difference, stop . Right now, and I mean right now , you're going to play the game. Use this

37. The Monty Hall Problem: Some Explanations The monty hall problem Some Explanations. If you don t know what theMonty Hall Let s Make a Deal problem is, start here. The Answer. http://www.rdrop.com/~half/Creations/Puzzles/LetsMakeADeal/explanations.html

MLI Home Creations Puzzles The Monty Hall Problem Some Explanations The Monty Hall Problem: Some Explanations If you don't know what the Monty Hall "Let's Make a Deal" problem is, start here. The Answer You'll do better on average if you switch. There is a 2/3 chance that the prize is behind the door you switched to, and only 1/3 that prize is behind your original door. Before I try to explain why, there are a few things will remain true throughout the following discussion: The host and assistants never lie or cheat. The prize is placed behind one door and not moved. You do not know where the prize is. Random numbers are truly random. Dice are fair. Two Common Misconceptions There seem to be two reasons for thinking the chance of picking the door with the prize is 50%. After one door has been revealed, there are two doors left, and the prize is behind one of them. Hence there must be a 50/50 chance of it being behind either unopened door. There are four possible outcomes (to be shown later). Two are winning outcomes if you stay, two if you switch. So there are 2 out of 4 winning cases if you either stay or switch. That means there is a 50/50 chance of winning with either strategy. I'll tackle these misconceptions in order.

38. Welcome To Monty Hall! The socalled monty hall problem is an ancient net.chestnut which, every time itappears on the net ignites mega-flame wars and consumes enormous bandwidth as http://www.sover.net/~nichael/puzzles/monty/

Welcome to Monty Hall The so-called Monty Hall Problem is an ancient net.chestnut which, every time it appears on the net ignites mega-flame wars and consumes enormous bandwidth as folks wrangle (once again) over the problem and its solution. The following is an attempt to supply an introduction to the problem (in case you haven't seen it before) and provide a reasonable and clear explanation of the answer. The Problem A Hint The Solution Return to Nichael Cramer's HomePage ... nichael@sover.net

39. Empirical Proof Of The Monty Hall Problem - Encyclopedia Article About Empirical encyclopedia article about Empirical proof of the monty hall problem. Empiricalproof of the monty hall problem. Word Word. http://encyclopedia.thefreedictionary.com/Empirical proof of the Monty Hall prob

Dictionaries: General Computing Medical Legal Encyclopedia Empirical proof of the Monty Hall problem Word: Word Starts with Ends with Definition The purpose of the following Perl Perl , also Practical Extraction and Report Language (a backronym, see below), is a programming language released by Larry Wall on December 18, 1987 that borrows features from C, sed, awk, shell scripting (sh), and (to a lesser extent) from many other programming languages as well. Rationale Perl was designed to be a practical language to extract information from text files and to generate reports from that information. One of its mottos is "There's more than one way to do it" (TMTOWTDI - pronounced 'Tim Toady'). Another is Click the link for more information. program is to prove the result to the Monty Hall problem 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? Click the link for more information.

40. Monty Hall Problem - Encyclopedia Article About Monty Hall Problem. Free Access, More results from encyclopedia.thefreedictionary.com Mathematically Interesting Games The Car and the Goats not get opened immediately. Instead, the host (Monty Hall) will openone of the other doors to reveal a goat. He will then give http://encyclopedia.thefreedictionary.com/Monty Hall problem

Dictionaries: General Computing Medical Legal Encyclopedia Monty Hall problem Word: Word Starts with Ends with Definition Please refer to that page if you wish to second or contest the nomination. The Monty Hall problem is a puzzle in probability The word probability derives from the Latin probare (to prove, or to test). Informally, probable is one of several words applied to uncertain events or knowledge, being more or less interchangeable with likely risky hazardous uncertain , and doubtful , depending on the context. Chance odds , and bet are other words expressing similar notions. As with the theory of mechanics which assigns precise definitions to such everyday terms as work and force , so the theory of probability attempts to quantify the notion of probable Click the link for more information. that is loosely based on the American For other uses see United States (disambiguation) The United States of America U.S.A. ), also referred to as the United States U.S. America the States , is a federal republic in North America and the Pacific Ocean (the islands of Hawaii, and the Aleutians). It extends from the Atlantic coast in the east to the Pacific Ocean in the west. It shares land borders with Canada in the north and Mexico in the south, shares a marine border with Russia in the west, and has a collection of districts, territories, and possessions around the world including Puerto Rico, Midway Atoll, and Guam. The country has fifty states, which have a level of local autonomy. A United States citizen is usually identified as an

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