81. [es] - Interesantan Zadatak (The Monty Hall Problem) icon Interesantan zadatak (The monty hall problem), 14.01.2004. u 1025. iconRe Interesantan zadatak (The monty hall problem), 14.01.2004. u 1059. http://www.elitesecurity.org/tema/39695

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82. Monty Hall Problem Simulation monty hall problem. At The question is Is is advantageous to switch,or does it not matter? This is the monty hall problem. The http://www.u.arizona.edu/~vmiller/applets/montyhall/MontyHallProblem.php

Monty Hall Problem At the end of each episode of Let's Make a Deal , the host, Monty Hall, would give the player with the most winnings a chance to bet it all on a prize between one of three doors. The player guessed the door he or she thought the prize was behind. Then Monty would open one of the other doors behind which contained a goat or demolished car or something, showing that the prize is not behind that door. Then he gave the player a chance to switch his or her guess or stay with the original door. The question is "Is is advantageous to switch, or does it not matter?" This is the Monty Hall Problem. The answer is that the player should switch. The probability of staying and winning is 1/3, and the probability of switching and winning is 2/3. Try this applet that simulates the game to see for yourself. Still not convinced? You may have gone on a winning/losing streak with the applet or you didn't play enough times to see that the probabilities converge to 2/3 for switching and 1/3 for staying. Below is a simulation in which one player always switches and one always stays. They each play 3 games per second so you'll be able to see the probabilities settle around their correct values. Always Switches Always Stays Win Ratio Win Ratio Home Programs

83. Factoids > Probability Paradoxes The monty hall problem; Cleaner power causes cancer problem. InevitableIllusions. Grand Finale; The WWW Tackles The monty hall problem. http://www-users.cs.york.ac.uk/~susan/cyc/p/prob.htm

probability paradoxes People seem to have very poor intuition about probability. It can take a lot of training to learn how to calculate probabilities correctly. The Monty Hall problem Cleaner power causes cancer problem Any probabilistic intuition by anyone not specifically tutored in probability calculus has a greater than 50 percent chance of being wrong. Piattelli-Palmarini. Inevitable Illusions The Monty Hall, or "Three Boxes", problem You are on a Game Show, and there are three boxes in front of you. Your host, Monty Hall, tells you that one of the boxes contains a valuable prize, and that the other two are empty. He explains the rules: you get to choose a box, then he will open one of the remaining boxes to show it is empty, and then you will be offered the chance to change your choice to the remaining closed box, or stick with your original choice. You choose a box. Monty, who knows where the prize is, opens one of the other two boxes, as promised, and shows you that it is empty. Should you change, or stick? This problem causes massive debate whenever it is aired. Many people's intuition runs: "There are now two boxes, with an equal chance of holding the prize, so it makes no difference if I change or stick". However, the correct solution is "I had a one in three chance of getting the right box originally, so there is a two in three chance that the prize in in one of the other boxes. It's not in the one the host opened, so there is a two in three chance of it being in the other unopened box. I should change my choice and double my chances of winning."

84. Bricoleur: Webified Monty Hall Problem January 30, 2003 Webified monty hall problem. A webified versionof the monty hall problem via anil dash s daily links. Posted http://www.bricoleur.org/archives/000136.html

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85. 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?

86. 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.org/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.

87. 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 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.

88. 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

89. Cheap Monty Hall Fully HTMLbased simulator for the problem. All on one page. http://www.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?

90. Monty Hall monty hall. It s that time in the semester when I have to teach probability.I like to start by driving people crazy with the Let s Make a Deal problem. http://cuwu.editthispage.com/stories/storyReader$144

Home FAQ Feedback Statistical Links ... Courses using Weblogs Members Join Now Login Monty Hall Posted by John Marden , 2/28/00 at 1:46:25 PM. Monty Hall It's that time in the semester when I have to teach probability. I like to start by driving people crazy with the Let's Make a Deal problem. Here's the setup: There are three boxes, one which contains a New Car!!!! You pick one. Monty knows which one contains the car. He opens (one of the) empty ones. You get a choice of Keeping your original box. Trading for the one left unopened. Which gives you a better chance of winning, keeping or trading? Or do they have the same chance, being as how there are only two boxes left? Some arguments . (The answer Try it out: Chance News' take on it. There are lots of other Websites on this problem, but I like the Car Talk guys' best (especially when you don't actually have to listen to them): About Statistics The Ants are My Friend Trade . Try this to maybe convince yourself. In the applet, first decide what your strategy is, then pick a box. Then press the "Cheat" button. Now you can see whether you win or lose without playing out the game. If your strategy is to keep, under what circumstances do you win? If your strategy is to trade, under what circumstances do you win? That is, if you

91. The Straight Dope: On "Let's Make A Deal," You Pick Door #1. Monty Opens Door #2 To beat the dead horse of monty hall s gameshow problem Marilyn was wrong,and you were right the first time Eric Dynamic, Berkeley, California. http://www.straightdope.com/classics/a3_189.html

Home Page Message Boards News Archive ... FAQs, etc. On "Let's Make a Deal," you pick Door #1. Monty opens Door #2no prize. Do you stay with Door #1 or switch to #3? 02-Nov-1990 Dear Cecil: I was perversely flipping through the Parade section of my Sunday newspaper when I stumbled upon Marilyn vos Savant's "Ask Marilyn" column. Even more perversely, I read it. It wasn't a total loss, though, because it appears she made another mistake, even worse than the one you pointed out in a very entertaining column a few months ago. Here's the 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 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? ANSWER: Yes; you should switch. The first door has a one-third chance of winning, but the second door has a two-thirds chance. Here's a good way to visualize what happened. Suppose there are a million doors, and you pick door No. 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? Correct me if I'm wrong, Cecil, but aren't the odds equal for the remaining doorsone in two? Michael Grice, Madison, Wisconsin

92. Drei-Kasten-Problem – Drei-Türen-Problem – Monty-Hall-Problem – Gefangenenpr Translate this page Drei-Kasten-problem – Gefangenenproblem – Drei-Türen-problem – monty-hall-problemSeit dem Calcul des Probabilités, 1889, von Bertrand taucht dieses http://www.gavagai.de/themen/HHPT09.htm

Seit dem , 1889, von Bertrand taucht dieses Paradox mit verschiedener Geschichte immer wieder auf Drei-Kasten-Problem von Joseph L. F. Bertrand ( Biografie ) oder Bertrands Schachtelparadoxon Stochastik, Leistungskurs , siehe Literatur Drei-Gefangenen-Problem Das Problem tauchte in neuem Gewand von Martin Gardner in der Oktober 1959 Ausgabe des Scientific American wieder auf. Es wurde als "The Three Prisoner Problem" in Martin Gardner: More Mathematical Puzzles and Diversions , 1961, aufgenommen. The Colossal Book of Mathematics , siehe Literatur 1975 tauchte das Problem, angeregt von Monty Halls TV-Show "Let's Make a Deal", erneut in neuer Verpackung in der Zeitschrift The American Statistician Parade vor. Versteck der Andromeda Das Versteck der Andromeda. Neue Mathematische Kurzgeschichten , siehe Literatur Bertrand, Joseph Louis Francois mit dem nach ihm beannnten Drei-Kasten-Paradoxon. Eric Weisstein's World of Scientific Biography Academie Francaise Literatur Anfang

93. The Monty Hall Page Door 1 Door 2 Door 3 Behind one of these doors is a car. Behind the othertwo is a goat. Click on the door in which you think the car is behind. http://math.ucsd.edu/~crypto/Monty/monty.html

Behind one of these doors is a car. Behind the other two is a goat. Click on the door in which you think the car is behind. Back Home Programs Documentation ... People

94. The Monty Hall Page Play the Game. An Explanation of the game. Back Home Programs Documentation Internet People http://euclid.ucsd.edu/~crypto/Monty/Montytitle.html

Play the Game An Explanation of the game Back Home Play the Game An Explanation of the game Back Home ... People

95. Let S Make A Deal hall is telling the contestant where the car is! How does this problemchange if monty hall does not know where the car is located? http://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 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 (ie. a car) behind one of the doors and a not-so-nice prize (ie. 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.

96. Monty Hall, 3 Doors http://www.shodor.org/interactivate/activities/monty3/

If you are using one of these browsers, it is likely that you do not have JavaScript enabled. Please enable it under Options/Preferences in your browser's menu. Please help us by suggesting enhancements or reporting bugs in this program. Or, send us other questions or comments about this activity. The Shodor Education Foundation, Inc.

97. Advanced Monty Hall You need to have a Java enabled browser to view this Java applet.If your browser supports Java, but you are seeing this mesasge http://www.shodor.org/interactivate/activities/montynew/

You need to have a Java enabled browser to view this Java applet. If your browser supports Java, but you are seeing this mesasge, you probably need to enable Java Please help us by suggesting enhancements or reporting bugs in this program. Or, send us other questions or comments about this activity. The Shodor Education Foundation, Inc.

98. Monty Hall Simulation Please be patient while the program loads. If part of it disappears whilerunning, jiggle the window size. Close this window when you are done. http://people.hofstra.edu/staff/steven_r_costenoble/MontyHall/MontyHallSim.html

Please be patient while the program loads. If part of it disappears while running, jiggle the window size. Close this window when you are done. Sorry, but you need a Java-enhanced browser to use this simulation.

99. The Let's Make A Deal Applet clearly 2/3. Despite a very clear explanation of this paradox, moststudents have a difficulty understanding the problem. It is 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.

100. The Chronicle: Page Not Found The page you tried to retrieve could not be found. http//chronicle.com/0004/hypoextra.htmlPlease help us fix any broken links http://linguafranca.com/0004/hypo-extra.html

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