61. The Monty Hall Problem The monty hall problem. Suppose you are a contestant on a game show.The host shows you three doors. Behind one door is a new car http://www.cs.queensu.ca/home/cisc365/1998Dawes/monty.html

The Monty Hall Problem Suppose you are a contestant on a game show. The host shows you three doors. Behind one door is a new car - behind the other doors there are goats. The host knows where the car is, but you of course do not. The host asks you to pick one of the doors. Before your door is opened, the host opens one of the other doors and shows you that there is a goat there. She then offers to let you trade your door (still unopened) for the other unopened door. Should you keep your first choice, trade for the other door, or does it make any difference at all? A hint: there are 2 closed doors left, and the car could be behind either of them. Note: This assumes that you would rather have a car than a goat. If this is not the case, please replace all references to "car" by something that would appeal to you more than a goat.

62. A Simulation Of The Monty Hall Problem The monty hall problem The applet below simulates the monty hall problem.In one form of the problem, there are three doors, two http://www.cs.cmu.edu/~donna/personal/MontyHall/

The Monty Hall Problem The applet below simulates the Monty Hall problem. In one form of the problem, there are three doors, two of which have goats behind them, and one of which has a million dollars behind it. You choose one of the doors, and then Monty opens one of the other doors, revealing a goat. He then asks if you want to switch to the remaining door. This applet simulates the number of wins you will have if you switch, or if you don't switch. In another form of the problem, Monty chooses between the remaining doors randomly. If he opens the door with a million dollars, you lose. If he picks a goat, you can then either switch your door or not. You can choose which form of the game to simulate by using the second group of radio buttons. Additionally, you can see what happens in each game by selecting the checkbox.

63. The Monty Hall Problem http://www.wi.leidenuniv.nl/home/jeggermo/Monty_Hall/english/

64. Math Alive 199 Lab 3 monty hall problem (page 1 of 2) Trying to find the best strategyto win in this game is a famous brain teaser, not least http://www.princeton.edu/~matalive/VirtualClassroom/v0.1/html/lab3/lab3_1.html

Math Alive Table Of Contents Lab 3: Probability and Statistics Monty Hall Problem Disease Testing Experiment Statistical Calculations Confidence Interval ... Histogram Lab 3: Monty Hall Problem (page 1 of 2) Trying to find the best strategy to win in this game is a famous brain teaser, not least because so many people (including mathematicians) get it wrong. The game is very simple: you are shown three closed doors. Behind one of them is a car, behind the two others, a cow. You first pick one door, but it does not open right away. The game host, Monty Hall, who knows behind which door the car is waiting, then teases you by opening one of the two doors that you had not picked to show you the cow sitting there. Then he may offer you a choice: staying with your original pick, or switching to the third remaining door. Should you switch or shouldn't you? Well, it really all depends! Below, you'll play this game in three different versions, with three different hosts. Host 1 always offers you the possibility to switch after he has opened one of the doors you didn't pick which has a cow. Host 2 offers that choice only some of the time; his decision to do so depends on the door you picked on the first go. You'll have to find out what his rule for deciding is.

65. 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://www.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.

66. The Car-and-Goats (Monty Hall) Problem The Car and Goats (Monty Hall) Problem. Back to Handout Index. This problem istherefore known as the carand-goats problem or the monty hall problem. http://members.aol.com/cebarat/vsu/stat330/handout/cargoats.htm

67. 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

68. FAQ-13 What Is The Answer To The Monty Hall, Envelope, Or Birthday Problem? 13 What is the answer to the Monty Hall, Envelope, or Birthday problem? Thereis a classic probability puzzle, which is called the monty hall problem. http://www.cmh.edu/stats/faq/faq13.asp

13 What is the answer to the Monty Hall, Envelope, or Birthday problem? There is a classic probability puzzle, which is called the Monty Hall problem. Here's a nice description from the rec.puzzles FAQ. "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 general consensus is that the probability of winning the car is 1/3 if you don't switch and 2/3 if you do switch. But there are some implicit assumptions in this problem that cause a raging debate every time it appears on STAT-L. For example, the host may be perversely trying to goad you into a bad switch and reveals a door only when your current door has a car behind it. There are at least thirty web sites that discuss this problem. Here are three good sites: http://www.smartpages.com/faqs/sci-math-faq/montyhall/faq.html

69. The Monty Hall Problem The monty hall problem. Scenario. We play a game with three cards,one red and two black. I mix the cards and hold them up so that http://www.onid.orst.edu/~robsonr/probpark/unexpected/montyhall.html

MM_preloadImages('cardback.gif'); MM_preloadImages('cardback.gif','cardback.gif'); MM_preloadImages('cardback._grey.gif'); The Monty Hall Problem. Scenario. We play a game with three cards, one red and two black. I mix the cards and hold them up so that I can see them and you cannot. You point to one card and win if the card is red. To make things a little more interesting, after you have made your choice I show you a black card from among the two you have not chosen and put it down on the table. I now have two cards left in my hand: one is the one you have chosen and the other is not. I then offer you the opportunity to switch your choice. To see how this works, try it yourself below. CARD # 1 CARD # 2 CARD # 3 STEP 1: STEP 2: PICK A CARD CARD #1 CARD #2 CARD #3 STEP 3: STEP 4: OPTIONAL: STEP 5: (You win if the card is red.) Question: Does switching cards increase, decrease, or leave unchanged your chances of winning? (Choose your answer and type your explanation in the box below) Decreases Chances of Winning Doesn't Effect Chances Increases Chances of Winning.

70. STAT100 Computer Programs Monty Hall. Games, The monty hall problem, drawing poker hands (just watchingthem), and matching correlation coefficients to scatter plots. Help, http://www.stat.uiuc.edu/~stat100/cuwu/

The CUWU Statistics Program 2000 version The choices: Analyze data Perform some simple data analyses: Basic statistics, histograms, "split" histograms, scatter plots and regression, calculations. Box Models Does simulations of drawing tickets out of a box. Illustrates the central limit theorem, confidence intervals, the law of averages. Monty Hall Games The Monty Hall Problem, drawing poker hands (just watching them), and matching correlation coefficients to scatter plots. Help Guessing correlations: If you are an instructor and would like to set up a group so that your students can compete among themselves, send a request to stat100@stat.uiuc.edu , along with a name for your group. To compete against your group: Type in your group id, then press "Go": I've taken away competing against the world because I don't have time to fix the scores when clever people hack them. CyberStats is a completely web-based statistics course. Download the program. There is a zip file, and a self-extracting zip file. The latter is easier for Windows95/NT. See the readme file.

71. Wisdom And Short Stories - The Monty Hall Problem - There Are Three Doors On Sta The monty hall problem. This rather interesting problem arises froma game show, Monty Hall is the host.. There are three doors on http://www.davidpbrown.co.uk/Wisdom/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.

72. The Monty Hall Problem The monty hall problem. The game show Lets Make a Deal was played as followed.A contestant was asked to choose between three closed doors. http://home.sprintmail.com/~dovi/c /unit2/monty.htm

73. Ailanto : The Monty Hall Problem the monty hall problem. supren hejmen In September 1991 a readerof Marilyn Vos Savant's Parade column asked the following question http://www.kafejo.com/iq/3doors.htm

The Monty Hall Problem supren hejmen In September 1991 a reader of Marilyn Vos Savant's Parade column asked the following 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's conclusion was that one should switch. The confusion arises thus... The game is really two games! The first game is a three-door problem. Your odds of choosing correctly are 1 in 3. The second game is a two-door problem. Your odds of choosing correctly are 1 in 2. Because your odds are worse in the first game, any choice in the first game is more likely to be incorrect than any choice in the second. Marilyn and friends therefore say that you should switch. But they're comparing apples and oranges. The probability for a door in the first game cannot be applied to the same door in the second game; it's a new game! The odds for all remaining doors increase when a door is removed from play. The door selected in the first game, which had a 1/3 chance, has a 1/2 chance in the second game.

74. Education, Mathematics, Fun, Monty Hall Dilemma Numbers makes use of the monty hall Dilemma to demonstrate a mathematician's approach to problem solving. First run 50 http://www.cut-the-knot.com/hall.html

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Monty Hall Dilemma The Monty Hall Dilemma was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996. Marylin received the following 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker Columbia, MD Marylin's response caused an avalanche of correspondence, mostly from people who would not accept her solution. Several iterations of correspondence ensued. Eventually, she issued a call to Math teachers among her readers to organize experiments and send her the charts. Some readers with access to computers ran computer simulations. At long last, the truth was established and accepted. Below is one simulation you may try on your computer. For simplicity, I do not hide goats behind the doors. There is only one 'abstract' prize. You may either hit on the right door or miss it. You make your selection by pressing small round buttons below input controls that substitute for the doors. Down below other controls update experiment statistics even as you progress.

75. The Monte Hall Problem Goto K. Related Bookmarks. For a great description of the Monte hallproblem, visit monty hall (Let's Make a Deal) problem. To see http://math.rice.edu/~hemphill/Professional/Presentations/MonteHall/Monte.html

The Monte Hall Problem Boyd E. Hemphill of The John Cooper School and Dennis Donovan of The Galveston Bay Project Presented at The 10th Anniversary Celebration of The Rice University School Math Project Description of Problem Game Program (Montesim) Rapid Simulation (Monte) ... Related Bookmarks Description of Problem The infamous probabalistic conundrum that has come to be know as "The Monte Hall Problem" has its history in the game show Let's Make A Deal. Here is the infamous Monte Hall problem, as it appeared in Parade Magazine (September 1990): 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He then says to you, ``Do you want to pick door number 2?'' Is it to yo ur advantage to switch your choice? Question #1: Does it matter if you change your mind? Question #2: What is the probabilty of winning if your remain with door number one? Quesiton #3: What is the probability of winning if your change your mind to door number two?

76. Education, Mathematics, Fun, Monty Hall Dilemma Remark 2. SK.Stein in his book Strength in Numbers makes use of the monty HallDilemma to demonstrate a mathematician's approach to problem solving. http://www.cut-the-knot.com/hall.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Monty Hall Dilemma The Monty Hall Dilemma was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996. Marylin received the following 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker Columbia, MD Marylin's response caused an avalanche of correspondence, mostly from people who would not accept her solution. Several iterations of correspondence ensued. Eventually, she issued a call to Math teachers among her readers to organize experiments and send her the charts. Some readers with access to computers ran computer simulations. At long last, the truth was established and accepted. Below is one simulation you may try on your computer. For simplicity, I do not hide goats behind the doors. There is only one 'abstract' prize. You may either hit on the right door or miss it. You make your selection by pressing small round buttons below input controls that substitute for the doors. Down below other controls update experiment statistics even as you progress.

77. Education, Mathematics, Fun, Monty Hall Dilemma Includes the original question posed to Marylin vos Savant about the problem, a simulator, solutions and other information on the problem. http://www.fortunecity.com/victorian/vangogh/111/9.htm

web hosting domain names email addresses related sites Monty Hall Dilemma The Monty Hall Dilemma was discussed in the popular "Ask Marylin" question-and-answer column of the Parade magazine. Details can also be found in the "Power of Logical Thinking" by Marylin vos Savant, St. Martin's Press, 1996. Marylin received the following 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 number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors? Craig. F. Whitaker Columbia, MD Marylin's response caused an avalanche of correspondence, mostly from people who would not accept her solution. Several iterations of correspondence ensued. Eventually, she issued a call to Math teachers among her readers to organize experiments and send her the charts. Some readers with access to computers ran computer simulations. At long last the truth was established and accepted. Below is one simulation you may try on your computer. For simplicity, I do not hide goats behind the doors. There is only one 'abstract' prize. You may either hit on the right door or miss it. You make your selection by pressing small round buttons below input controls that substitute for the doors. Down below other controls update experiment statistics even as you progress.

78. Monty Hall Puzzler: Historical Proof Benjamin King pointed out the critical assumpitons about monty hall's behaviorthat are necessary to solve the problem, and emphasized that the prior http://cartalk.cars.com/About/Monty/proof.html

Excerpted from The American Statistician, August 1975, Vol. 29, No. 3 On the Mony Hall Problem I have received a number of letters commenting on my "Letters to the Editor" in The American Statistician of February, 1975, entitled "A Problem in Probability." Several correspondents claim my answer is incorrect. The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random. An alternative solution to enumerating the mutually exclusive and equally likely outcomes is as follows: A = event that keys are contained in box B B = event that contestant chooses box B C = event that Monty Hall opens box A Then = P(ABC)/P(BC) If the contestant trades his box B for the unopened box on the table, his probability of winning the card is 2/3. D.L. Ferguson presented a generalization of this problem for the case of n boxes, in which Monty Hall opens p boxes. In this situation, the probability the contestant wins when he switches boxes is (n-1)/[n(n-p-1)]. Benjamin King pointed out the critical assumpitons about Monty Hall's behavior that are necessary to solve the problem, and emphasized that "the prior distribution is not the only part of the probabilistic side of a decision problem that is subjective."

79. Cheap Monty Hall Fully HTMLbased simulator for the problem. All on one page. http://utstat.toronto.edu/david/MH.html

THE MONTY HALL PROBLEM The following is a simple simulation of the Monty Hall problem. It took a total of 1.5 hours to create. Adding colour and graphics would be simple but the time might better be spent on other examples. The names of links should be changed and the file tripled in size. We haven't spent much time on the words here so read the first few pages carefully. Grab a paper and pencil and remember, looking at the scroll bars is cheating. David Andrews 6:31 p.m. June 5, 1996 START MONTY HALL There are three doors. Behind one is a car, behind the others are goats. For the moment, think that cars are handy and goats are a lot of work. Imagine that you want the car. This, of course, is subject to debate, but this is only a game. The debate comes after. Pick a door. Door 1 Door 2 Door 3 MONTY HALL You picked Door 1. Monty Hall has opened Door 3. It's not a car. But he gives you another chance. You can repick Door 1 or the other door. Should you stick or switch? That is the question. It is interesting to try both strategies. Which one is better?

80. Monty Hall - Explanations Of Solution Gives 4 explanations of the solution to this problem. http://exploringdata.cqu.edu.au/montyexp.htm

From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/ © Education Queensland, 1997 Monty Hall Puzzle - Explanations of the Solution One interesting aspect of this puzzle is that no one explanation seems to satisfy everybody. If you want to convince an entire class of skeptical students, you will need all of the solutions below, at least. Explanation 1 - my favourite The probability that the contestant chose the correct door initially is 1/3, since there are three doors each of which has an equal chance of concealing the prize. The probability that the door Monty Hall chooses conceals the prize is 0, since he never chooses the door that contains the prize. Since the sum of the three probabilities is 1, the probability that the prize is behind the other door is 1 - (1/3 + 0), which equals 2/3. Therefore the contestant will double the chance of winning by switching. Explanation 2 - looking at an extreme case Most people who get this puzzle wrong reason that after Monty reveals a losing door there are two doors left, one of which contains the prize, and therefore the probability of each concealing the prize is 1/2. This explanation dispels that line of reasoning. Imagine that there were a million doors. Monty knows which door conceals the prize, so he then opens 999 998 losing doors. You are now confronted with two doors, the one you chose initially and the one Monty has left. Do

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