41. Monty Hall Problem Harvard - A D Wholesale Welcome to A D Wholesale. We are among the top distributors of candy and tobacco in the nation. Our competitive prices and unbeatable customer care have http://adwholesale.com/o2HcGiFJa/

42. Monty Hall Problem: Information From Answers.com Monty Hall problem The Monty Hall problem can be solved empirically using computer programs Empirical solution of the Monty Hall problem (C) http://www.answers.com/topic/monty-hall-problem-1

43. Monty Hall 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 http://www.maa.org/devlin/devlin_07_03.html

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. In the 1960s, there was a popular weekly US television quiz show called

44. John Kay - The Monty Hall Problem - A Summing Up Aug 31, 2005 The Monty Hall problem. I have received a large correspondence on Monty Hall And here is what John Kay thinks of the Monty Hall problem. http://www.johnkay.com/2005/08/31/the-monty-hall-problem-a-summing-up/

@import url( http://www.johnkay.com/wp-content/themes/johnkay/style.css ); John Kay Contact Us About News ... Advanced Search 31 August 2005, Financial Times The Monty Hall problem I have received a large correspondence on Monty Hall, which has been extremely instructive (at least for me) in elucidating not just the Monty Hall question itself, which is of no consequence, but how we model business decisions more generally. The central reason the problem seems complex, and is so controversial, is the difficulty of establishing, or agreeing, on the extent to which a particular mathematical representation of a real problem accurately describes that problem. This issue is fundamental to all analytic approaches to decision making. There are three broad approaches to solution. The first (which generates the standard ‘correct’ answer, which is to switch) seeks for the single most plausible representation of the problem. In this representation, Monty knows which box has the car, is obliged to open one of the boxes, and chooses at random between these boxes which have not been chosen and do not contain the car. However this is only one possible account of Monty’s motives and behaviour. There are other, perhaps less plausible, accounts. That leads directly to a second approach to the problem, which is to attempt to construct an exhaustive list of every possible complete description of the problem. This involves speculation about the possible states of Monty’s knowledge, Monty’s motives, and in turn requires us to take a view of Monty’s expectations of the contestant’s behaviour. There is generally no way of establishing whether or not such a list of possible descriptions is truly exhaustive.

45. UBB Message - Apologetics.com Forums 9 posts 5 authorsBut back to the Monty Hall Problem. A good way to understand problems like this is to push them to an extreme. Imagine, for example, that there are not 3 http://www.apologetics.com/forums/ubbthreads.php?ubb=showflat&Number=150414

46. Interactive Feature - The Monty Hall Problem - NYTimes.com An online game that let’s you try and win a (pretend) car and explains the best strategy for playing The Monty Hall Problem. http://www.nytimes.com/2008/04/08/science/08monty.html

47. The Let's Make A Deal Applet As a motivating example behind the discussion of probability, an applet has been developed which allows students to investigate the Let's Make a Deal Paradox. http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html

The Let's Make a Deal Applet As a motivating example behind the discussion of probability, an applet has been developed which allows students to investigate the Let's Make a Deal Paradox. This paradox is related to a popular television show in the 1970's. In the show, a contestant was given a choice of three doors of which one contained a prize. The other two doors contained gag gifts like a chicken or a donkey. After the contestant chose an initial door, the host of the show then revealed an empty door among the two unchosen doors, and asks the contestant if he or she would like to switch to the other unchosen door. The question is should the contestant switch. Do the odds of winning increase by switching to the remaining door? The intuition of most students tells them that each of the doors, the chosen door and the unchosen door, are equally likely to contain the prize so that there is a 50-50 chance of winning with either selection. This, however, is not the case. The probability of winning by using the switching technique is 2/3 while the odds of winning by not switching is 1/3. The easiest way to explain this to students is as follows. The probability of picking the wrong door in the initial stage of the game is 2/3. If the contestant picks the wrong door initially, the host must reveal the remaining empty door in the second stage of the game. Thus, if the contestant switches after picking the wrong door initially, the contestant will win the prize. The probability of winning by switching then reduces to the probability of picking the wrong door in the initial stage which is clearly 2/3.

48. Www.montyhallproblem.com The sci.math.faq on the Monty Hall Problem From version 7.5, dated 220-98 (Note This is an excerpt from the frequently asked questions the FAQ of the venerable http://www.montyhallproblem.com/mh-math-faq.html

The sci.math.faq on the Monty Hall Problem From version 7.5, dated: 2-20-98 (Note: This is an excerpt from the "frequently asked questions" the "FAQ" of the venerable USENET newsgroup "sci.math". The MHP is discussed there not infrequently.) The Monty Hall problem This problem has rapidly become part of the mathematical folklore. The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article. Problem A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car? If the host always opens one of the two other doors, you should switch. Notice that 1/3 of the time you choose the right door (i.e. the one with the car) and switching is wrong, while 2/3 of the time you choose the wrong door and switching gets you the car. Thus the expected return of switching is 2/3 which improves over your original expected gain of 1/3. Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.

49. Book Giveaway: The Monty Hall Problem : Science After Sunclipse Nov 17, 2009 I just noticed on my blag sidebar that the ScienceBorg Collective is offering ten free copies of Jason Rosenhouse s muchlauded book, http://scienceblogs.com/sunclipse/2009/11/book_giveaway_the_monty_hall_p.php

50. The Monty Hall Page In order to explain why the numbers are suggesting that it is better to switch, it's necessary to describe how the game is played. If you have never seen Monty Hall's Let's Make http://www.math.ucsd.edu/~crypto/Monty/montybg.html

In order to explain why the numbers are suggesting that it is better to switch, it's necessary to describe how the game is played. If you have never seen Monty Hall's Let's Make A Deal game show, then let me catch you up to speed. Let's Make A Deal Monty Hall I can only assume Monty Hall's game show Let's Make A Deal took place sometime during the sixties and/or seventies. Information on this particular game show has somehow eluded the internet and my less than vivid memory sometimes fails me, but the basic setup for the game is as follows. Pretty much the entire audience dresses up like a complete loon (Raggedy Ann and Andy were fairly popular costumes) hoping that Monty Hall would select them out of the crowd and offer them a chance to win a fabulous prize. For instance, he might offer you $100 for every paper clip that you have in your posession or he might give you $500, but then ask you if you would like to keep the money or trade it for what's in a particular box. Of course there could be $1000 in the box or a single can of dog food. Anyway, I'm digressing and hopefully you get the basic gist of the game. The particular game that we are concerned with here is where Monty Hall offers you the opportunity to win what is behind one of three doors. Typically there was a really nice prize (i.e., a car) behind one of the doors and a not-so-nice prize (i.e., a goat) behind the other two. After selecting a door, Monty would then proceed to open one of the doors you didn't select. It is important to note here that Monty would NOT open the door that concealed the car. At this point, he would then ask you if you wanted to switch to the other door before revealing what you had won.

51. The Famous Monty Hall Problem « Lawand's Blog May 19, 2008 I first knew about this while watching an episode of NUMB3RS, This dilemma is called the (Monty Hall problem) or (Monty Hall paradox) http://lawand.wordpress.com/2008/05/19/the-famous-monty-hall-problem/

Play Your Video As ASCII Art! 20Q Will Guess What You Are Thinking About, Can You Beat It? The Famous Monty Hall Problem Imagine that you where in a game show, and the host has offered you three doors to choose from, knowing that one contains a fancy car behind it and the other two are each hiding a not-so-fancy goat behind it! saying that you gain what is behind the door that you choose. Now after choosing a door and before opening it to see the result, the host opens another one containing a goat (he already knows that) and asks you if you want to change your selection! Now wait a minute, what does it matter if you switched to the other unopened door? Oops! you were wrong :) Demystification Now for the explanation of this dilemma check out this figure which is a tree showing the probability of every possible outcome if the player initially picks Door 1: All Possible Choices Monty Hall Wikipedia page I first knew about this while watching an episode of NUMB3RS, This dilemma is called the (Monty Hall problem) or (Monty Hall paradox) because the solution is counter-intuitive ( Monty Hall Petty weird huh?

52. Interactivate: Simple Monty Hall Simple Monty Hall Choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program Let's Make a Deal. http://www.shodor.org/interactivate/activities/SimpleMontyHall/

@import "/common-1.9/ui/default/css/main.css"; @import "/common-1.9/ui/interactivate/css/main.css"; @import "/interactivate/public/css/main.css"; @import "/common-1.9/ui/xforms/xforms.css"; Interactivate Jump To: Activities Discussions Lessons Tools Assessments Dictionary Textbooks Standards Version 1.0 Browse: By Subject (broad) By Topic (specific) By Audience By Resource Type Simple Monty Hall Shodor Interactivate Activities tab0 content Simple Monty Hall: Choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Staying or switching between the two remaining doors. On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment, faculty enhancement, and interactive curriculum development at all levels. Student development of numerical models and simulations integrated with core curriculum provides an opportunity to gain practical experience in computational science. Additionally, the National Computational Science Institute (NCSI) provides nation-wide workshops portraying resources and instructional ideas to middle school, high school, and undergraduate instructors for use in the classroom. Resources and materials offered to these instructors are available free of charge from Shodor's website and are largely developed by Shodor student interns. Shodor's academic program efficiently guides participants from excitement to experience to expertise through computational explorations, research opportunities, and service.

53. Marilyn Vos Savant | The Game Show Problem The problem and a discussion on the validity of the solution. http://www.marilynvossavant.com/articles/gameshow.html

Game Show Problem Printer-friendly version (This material in this article was originally published in PARADE magazine in 1990 and 1991.) 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 #1, and the host, who knows what's behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? Craig F. Whitaker Columbia, Maryland Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what's behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You'd switch to that door pretty fast, wouldn't you? Since you seem to enjoy coming straight to the point, I'll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error and in the future being more careful. Robert Sachs, Ph.D.

54. Jon Todd » The Monty Hall Problem Apr 9, 2008 The Monty Hall Problem Explained. Suppose you re on a game show, and you re given the choice of three doors Behind one door is a car; http://www.jontodd.com/2008/04/09/the-monty-hall-problem/

55. Monty Hall Problem - Wolfram Demonstrations Project As a contestant on Monty Hall's game show, you are presented with three doors. Behind one door is a new car and behind each of the other two is a goat. http://demonstrations.wolfram.com/MontyHallProblem/

56. The Monty Hall Problem The Monty Hall Problem Suppose you're on a game show, and you're given the choice of three doors Behind one door is the Grand Prize; behind the others, Booby Prizes. http://www.hofstra.edu/~matsrc/MontyHall/MontyHall.html

57. Monty Hall Problem -- Math Fun Facts Here's a problem that makes the round every few years, and each time, it is hotly debated. You are on a game show. You are presented with a choice of 3 doors behind one http://www.math.hmc.edu/funfacts/ffiles/20002.6.shtml

hosted by the Harvey Mudd College Math Department Francis Su The Math Fun Facts App is now in the App Store Subscribe to our RSS feed or Any Easy Medium Advanced The Math Fun Facts App! List All List Recent List Popular ... Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Medium level: Monty Hall Problem Figure 1 Here's a problem that makes the round every few years, and each time, it is hotly debated. You are on a game show. You are presented with a choice of 3 doors: behind one is a luxury car, and behind the other two are nothing. The host asks you pick one of the doors. After you do this, as part of the game he opens one unpicked doors which he knows is empty. There are now only the door you picked and one remaining door which are unopened. You are asked if you would like to switch your choice. Should you switch? Presentation Suggestions: Another version of this problem uses cards in a game called "three-card monte", often played by scam artists on the streets of New York who prey on easily-duped tourists. The Math Behind the Fact: The Monty Hall Problem, or Monty Hall Paradox, as it is known, is named after the host of the popular game show "Let's Make a Deal" in the 1960's and 70's, who presented contestants with exactly this scenario. The answer is YES, you should switch, because the probability that you will find the car by doing so is 2/3. This is because the

58. Visualizing The Monty Hall Problem « Greatplay.net Apr 27, 2009 Visualizing the Monty Hall Problem. 17 April 2009, 1200 pm Now that you ve figured out the Monty Hall Problem, maybe you could go on to http://www.greatplay.net/?p=508

59. Monty Hall Problem The Problem. When the TV game show Let’s Make a Deal first aired on NBC in 1963, nobody could have predicted its impact on the academic fields of economics, mathematics http://leeps.ucsc.edu/misc/page/monty-hall-puzzle/

Home About People Projects ... Misc Learning and Experimental Economics Projects of Santa Cruz! Monty Hall Problem Papers and Documents Links Simulation and Activities Interesting Variants and Comments The Problem. When the TV game show As recounted by Barry Nalebuff in 1987, Monty Hall , the host of the television show, would always give the participant the option to switch from his initial choice, after Monty opened one of the unchosen doors to reveal a zonk. Nalebuff and later writers said that participants hardly ever accepted the option. Marilyn vos Savant in 1990, and she said Yes. She explained why switching doubled the probability of winning the valuable prize. Several readers, including PhD mathematicians, told Marilyn that she was ignorant or worse, and that participants had a 50-50 chance of winning whether or not they switched. Variants on her explanation can be found here and here Whatever its true historical basis, the Monty Hall Problem has been studied and debated intensively by a large and eclectic set of economists, mathematicians and psychologists, as early as . The purpose of this webpage is to collect and provide documents, links, simulations and activities on the Monty Hall Problem. We hope that it is useful to students, professors and journalists alike.

60. BBC/OU Open2.net - Mathematical Thinking - Monty Hall Problem An article on the Monty Hall problem, looking at chance and probability http://www.open2.net/sciencetechnologynature/maths/montyhallproblem2.html

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