1. Monty Hall Problem - Wikipedia, The Free Encyclopedia The Monty Hall problem is a probability puzzle loosely based on the American television game show Let s Make a Deal. The name comes from the show s original http://en.wikipedia.org/wiki/Monty_Hall_problem

Monty Hall problem From Wikipedia, the free encyclopedia Jump to: navigation search This page is currently protected from editing until November 8, 2010 or until disputes have been resolved. This protection is not an endorsement of the current version . See the protection policy and protection log for more details. Please discuss any changes on the talk page ; you may use the editprotected template to ask an administrator to make the edit if it is supported by consensus . You may also request that this page be unprotected. In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1. The Monty Hall problem is a probability puzzle loosely based on the American television game show Let's Make a Deal . The name comes from the show's original host, Monty Hall . The problem is also called the Monty Hall paradox , as it is a veridical paradox in that the result appears absurd but is demonstrably true. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. A well-known statement of the problem was published in

2. Monty Hall Problem - Definition In search of a new car, you pick door number 2, Monty then shows you the goat behind door number 1 and asks if you'd like to switch to door number three. http://www.wordiq.com/definition/Monty_Hall_problem

Monty Hall problem - Definition In search of a new car, you pick door number 2, Monty then shows you the goat behind door number 1 and asks if you'd like to switch to door number three. You have better odds if you do. 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 other two is a goat. The contestant is allowed to open one door, and will win whatever is behind the door he opens; however, after the contestant has selected a door but before he actually opens it, the host (who knows what is behind each door) opens one of the other doors to show that there is a goat behind it, and asks the contestant whether he wants to change his mind and switch to the other closed door. Does the contestant improve their chance of winning the car by switching or does it make no difference? The question has generated heated debate. As the solution appears to contradict elementary ideas of probability and common sense, it may be regarded as a paradox Contents showTocToggle("show","hide")

3. Monty Hall Problem - Simple English Wikipedia, The Free Encyclopedia The Monty Hall problem is a famous problem in probability (chance). The problem is based on a television game show from the United States, Let's Make a Deal. http://simple.wikipedia.org/wiki/Monty_Hall_problem

Monty Hall problem From Wikipedia, the free encyclopedia Jump to: navigation search The Monty Hall problem is a famous problem in probability (chance). The problem is based on a television game show from the United States Let's Make a Deal . It is named for the host of this show, Monty Hall In the problem, there are three doors. A car prize of high value) is behind one door and goats ( booby prizes of low value) behind the other two doors. First, the player chooses a door but does not open it. Then the host, who has knowledge of what is behind every door, opens a different door which he is certain has a goat behind it (opening either door with equal chances if the car is behind the player's door). Last, the host lets the player choose whether to keep what is behind the first door or to change choices to the third door (the one the host did not open). The rules of the problem are that the host has to open a door with a goat behind and has to let the player switch. The question is whether changing choices increases the chances of getting the car. The chances of the car being behind the two doors that are still closed seem equal, so most people say changing choices does not increase the chances of getting the car. The true answer is that changing choices increases the chances of getting the car from 1/3 (one out of three) to 2/3 (two out of three).

4. Monty Hall Problem - Rosetta Code Monty Hall problem You are encouraged to solve this task according to the task description, using any language you may know. http://rosettacode.org/wiki/Monty_Hall_problem

5. The Monty Hall Problem - A Game Simulation The Monty Hall Problem Illustration by a game simulation. http://www.userpages.de/monty_hall_problem/

The Monty Hall Problem Illustration by a game simulation Game simulation Contact Play mode self-play execute several game rounds per random generator Settings Summary Contact Originator of this Userpage: Dave Powered by

6. Monty Hall Problem - Uncyclopedia, The Content-free Encyclopedia The Monty Hall Problem is a mathematical question which has puzzled mathematicians for years. Its solution led to two now wellknown discoveries. The first is that in games of http://uncyclopedia.wikia.com/wiki/Monty_Hall_problem

7. Understanding The Monty Hall Problem | BetterExplained The Monty Hall problemhttp//en.wikipedia.org/wiki/monty_hall_problem is a counterintuitive statistics puzzle * There are 3 doors, behind which are two http://betterexplained.com/articles/understanding-the-monty-hall-problem/

@import url( http://betterexplained.com/wp-content/themes/be-v8/style.css ); BetterExplained Learn Right, Not Rote. Home All Posts About FAQ ... Understanding the Monty Hall Problem The Monty Hall problem is a counter-intuitive statistics puzzle: There are 3 doors, behind which are two goats and a car. why a simple game could be so baffling. The game is really about re-evaluating your decisions as new information emerges. Play the game Understanding Why Switching Works easier way: If I pick a door and hold, I have a 1/3 chance of winning. why Understanding The Game Filter There are 100 doors to pick from in the beginning You pick one door Monty looks at the 99 others, finds the goats, and opens all but 1 Do you stick with your original door (1/100), or the other door, which was filtered from 99? (Try this in the simulator game; use 10 doors instead of 100). improving Your decision: Do you want a random door out of 100 (initial guess) or the best door out of 99? Said another way, do you want 1 random chance or the best of 99 random chances? curated, filtered

8. The Monty Hall Problem - Associated Content - Associatedcontent.com Sep 8, 2009 I outline the infamous Monty Hall problem, show the correct solution in several ways, and review a book about the subject. http://www.associatedcontent.com/article/2151469/the_monty_hall_problem.html

AC.base_www = '/'; AC.base_adm = 'https://publish.associatedcontent.com/'; AC.base_img = 'http://i.acdn.us/'; AC.base_siteimg = 'http://i.acdn.us/siteimg/'; Associated Content Home Lifestyle Home Lifestyle ... Education The Monty Hall Problem Adjust font-size: Published September 08, 2009 by: Peter Flom View Profile Follow Add to Favorites ... Cba The World's Most Contentious Math Problem - Explained! The Monty Hall problem is, by far, the most contentious math problem ever. I will attempt to unravel some of its complexity, and I will also review a book about the problem. Here is how I will proceed: 1. Statement of the Monty Hall Problem and brief notes on history 2. The answer to the Monty Hall Problem 3. Intuitive approaches to the Monty Hall Problem 4. Monte Carlo/computer programming approaches to solving the Monty Hall Problem 5. A formal proof of the solution 6. A book review (beyond what's in the diary already) I'll mention right up front that the book was sent to me by Oxford University Press, it's called the Monty Hall Problem, the author is Jason Rosenhouse, and I liked it a lot. If you like this article, I think you'll like the book Statement of the Monty Hall problem You are on a game show. You are presented with three doors. Behind one of them is a car, behind the other two are goats. You get to choose a door. But before you open it, the host (Monty Hall), who knows where the car is, opens one of the other doors. He always opens a door with a goat. If both of the unchosen doors have goats, he picks one at random. The car was placed randomly, with 1/3 chance for each door.

9. The Monty Hall Problem - Math Images The Monty Hall Problem. The Monty Hall problem is a probability puzzle based on the 1960's game show Let's Make a Deal. When the Monty Hall problem was published in Parade Magazine http://mathforum.org/mathimages/index.php/The_Monty_Hall_Problem

The Monty Hall Problem From Math Images Jump to: navigation search Add to NSDL View in NSDL ... Edit Metadata The Monty Hall Problem Field: Algebra Image Created By: Grand Illusions The Monty Hall Problem The Monty Hall problem is a probability puzzle based on the 1960's game show Let's Make a Deal. When the Monty Hall problem was published in Parade Magazine in 1990, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine claiming the published solution was wrong. It remains one of the most disputed mathematical puzzles of all time. Contents Basic Description The Problem The Solution Aids to Comprehension ... Future Directions for this Page Basic Description The Problem The show's host, Monty Hall, asks a contestant to pick one of three doors. One door leads to a brand new car, but the other two lead to goats. Once the contestant has picked a door, Monty opens one of the two remaining doors. He is careful never to open the door hiding the car. After Monty has opened one of these other two doors, he offers the contestant the chance to switch doors. Is it to his advantage to stay with his original choice, switch to the other unopened door, or does it not matter? The Solution If you answered that the contestant's decision doesn't matter, then you are among about 90% of respondents who were quickly able to determine that the two remaining doors must be equally likely to hide the car. You are also wrong. The answer to the Monty Hall Problem is viewed by most people—including mathematicians—as extremely counter–intuitive.

10. Monty Hall Problem - Conservapedia The Monty Hall Problem is a basic example problem in statistic and probability theory based on the premise of the television show Let s Make http://www.conservapedia.com/Monty_Hall_problem

Monty Hall problem From Conservapedia Jump to: navigation search The Monty Hall Problem is a basic example problem in statistic and probability theory based on the premise of the television show Let's Make a Deal , originally hosted by Monty Hall Contents Problem Statement Solution Illustration using scenario outcomes Solution using Bayes' theorem Problem Statement A contestant on a game show is presented with three doors. Behind one of the doors is a car, and behind the other two doors are goats. The contestant chooses door 1. The host must then open a door to reveal a goat; he opens door 3. The host then gives the contestant a chance to switch his choice to door 2. If the contestant is trying to win the car, is it to his advantage to switch his choice? Solution It may be tempting to say that the contestant neither gains nor loses anything if he switches. Since there are two closed doors, and one of them is the winning door, it may appear that the probability of winning is 1/2 whether the contestant switches or not. Such reasoning is incorrect; the contestant always has a higher probability of winning if he switches. Illustration using scenario outcomes There are three possible scenarios in the problem.

11. Monty Hall Problem - Wikimedia In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 http://readerfeedback.labs.wikimedia.org/wiki/Monty_Hall_problem

Monty Hall problem From Wikimedia Jump to: navigation search In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1. The Monty Hall problem is a probability puzzle based on the American television game show Let's Make a Deal . The name comes from the show's host, Monty Hall . The problem is also called the Monty Hall paradox , as it is a veridical paradox in that the result appears absurd but is demonstrably true. The problem can be unambiguously stated as follows: 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. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice? ( Krauss and Wang 2003:10 As there is no way for the player to know which of the two remaining unopened doors is the winning door, most people assume that each of these doors has an equal probability and conclude that switching does not matter. In fact, the player should switch—doing so doubles the probability of winning the car from 1/3 to 2/3.

12. Visualizing The Monty Hall Problem : Programming May 5, 2009 Visualizing the Monty Hall problem (oscarbonilla.com). submitted 1 year ago by jbellis 33 comments; sharecancel. loading. http://www.reddit.com/r/programming/comments/8i3q3/visualizing_the_monty_hall_pr

13. The Monty Hall Problem - The Boston Globe Apr 19, 2010 Can you explain the famous Monty Hall problem, from the old �Let s Make a Deal TV show, involving contestants who guessed which of three http://www.boston.com/news/science/articles/2010/04/19/the_monty_hall_problem/

14. Monty Hall Problem Monty Hall problem The Monty Hall problem is a riddle in elementary probability that arose from the American game show Let's Make a Deal with host Monty Hall. http://www.fact-index.com/m/mo/monty_hall_problem.html

Main Page See live article Alphabetical index Monty Hall problem The Monty Hall problem is a riddle in elementary probability that arose from the American game show Let's Make a Deal with host Monty Hall . In spite of being an elementary problem, it is notorious for being the subject of controversy about both the statement of the problem and the correct answer. The problem is as follows: At the end of the show, a player is shown three doors. Behind one of them, there's a prize for him to keep, while the other two contain goats (signifying no prize to be won). Although the show host knows what is behind each door, of course the player does not. After the player makes a first choice, Monty opens one of the two other doors, revealing a goat. He then offers the player the option to either stick with the initial choice or switch to the other closed door. Should the player switch? The classical answer to this problem is yes , because the chances of winning the prize are twice as high when the player switches to another door than they are when the player sticks with their original choice. This is because upon the original choice, the player has only a 1/3 chance of choosing the door with the prize; this probability does not change when Monty opens a door with a goat. Hence the chances of winning the prize are 1/3 if the player sticks to their original choice, and thus 2/3 if the player switches. Table of contents 1 Assumptions 2 Aids to understanding 3 Variants 4 Origins ... 7 External Links Assumptions

15. Monty Hall Problem - Academic Kids In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3. http://www.academickids.com/encyclopedia/index.php/Monty_Hall_problem

Monty Hall problem From Academic Kids In search of a new car, the player picks door 3. The game host then opens door 1 to reveal a goat and offers to let the player pick door 2 instead of door 3. 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 player is shown three closed doors; behind one is a car, and behind each of the other two is a goat. The player is allowed to open one door, and will win whatever is behind the door. However, after the player selects a door but before opening it, the game host opens another door to reveal a goat. The host then offers the player an option to choose the other closed door. Does switching improve the player's chance of winning the car? With the assumptions explicitly stated below, the answer is yes The problem is also called the Monty Hall paradox , in the sense that the solution is counterintuitive, although the problem is not a logical self-contradiction. It has generated heated debate. Contents showTocToggle("show","hide")

16. Monty Hall Problem In search of a new car, the player picks door 1. The game host then opens door 3 to reveal a goat and offers to let the player pick door 2 instead of door 1. http://schools-wikipedia.org/wp/m/Monty_Hall_problem.htm

Monty Hall problem 2008/9 Schools Wikipedia Selection . Related subjects: Mathematics In search of a new car, the player picks door 1. The game host then opens door 3 to reveal a goat and offers to let the player pick door 2 instead of door 1. The Monty Hall problem is a puzzle involving probability loosely based on the American game show Monty Hall. The problem is also called the Monty Hall paradox ; it is a veridical paradox in the sense that the solution is counterintuitive. A widely known statement of the problem appeared in a letter to Ask Marilyn column in Parade 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? (Whitaker 1990) Because there is no way for the player to know which of the two unopened doors is the winning door, nearly all people assume that each door has an equal probability and conclude that switching does not matter. In fact, in the usual interpretation of the problem the player should When the problem and the solution appeared in Parade , approximately 10,000 readers, including several hundred mathematics professors, wrote to the magazine claiming the published solution was wrong. Some of the controversy was because the

17. Robson » Code » PHP » Monty Hall Problem this script simulates the monty hall problem http//en.wikipedia.org/wiki/ monty_hall_problem function monty_hall_problem($output=1, $switch=1) http://iceyboard.no-ip.org/projects/code/php/monty_hall_problem/

Robson Code PHP I, the creator of this work, hereby release this into the public domain. This applies worldwide. In case this is not legally possible, I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law. - Robson this script simulates the monty hall problem: http://en.wikipedia.org/wiki/Monty_Hall_problem 1. it does one example with and without switching 2. then it does a large number with and without switching and shows the results // seed the random number generator srand // output = whether to output information as the script runs // switch = whether to switch when the host shows a donkey function $output $switch // there are two donkeys and one car $prizes array 'donkey' 'donkey' 'car' // shuffle the prizes so they appear in a random order shuffle $prizes // print out the order if $output echo 'doors: ' implode $prizes // the player selects a random door $player $prizes // show the door the player picked and what is behind it if $output echo $player $prizes $player // now find a door with a donkey for the host do // choose random door for the host $host $prizes // check if the door isn't the players and contains a donkey // if not, continue selecting random doors until a valid one is found

18. Monty Hall Problem Monty Hall problem. A puzzle in probability that was inspired by the American game show Let s Make a Deal, hosted by Monty Hall. http://www.daviddarling.info/encyclopedia/M/Monty_Hall_problem.html

A B C D ... CONTACT entire Web this site Monty Hall problem A puzzle in probability that was inspired by the American game show "Let's Make a Deal," hosted by Monty Hall. In its original form it goes like this: at the end of the show, you, the player, are shown three doors. Behind one of them is a new car, behind the other two are goats. Monty knows where the car is, but you don't. You choose a door. Before that door is opened however, Monty opens one of the two other doors with a goat behind it. He then gives you the option of switching to the other closed door. Should you switch or stick? At first glance, it seems as if it shouldn't make any difference. But the answer is surprising. In another variation of the problem, consider that in the actual game show there were two contestants. Both of them were allowed to pick a door but not the same one. Monty then eliminated a player with a goat behind their door (if both players had a goat, one was eliminated randomly, without letting the players know about it), opened the door and then offered the remaining player a chance to switch. Should the remaining player switch? The answer is no. The reason: a switcher in this game will lose if and only if either of two initial choices of the two contestants was correct. How likely is that? Two-thirds. A sticker will win in those 2/3 of the cases. So stickers will win twice as often as switchers.

19. Monty Hall Problem - LogicWiki Aug 7, 2006 The Monty Hall Problem is a famous example of a problem that can be solved by Bayes Theorem. It is another excellent example of Bayes http://kleene.ss.uci.edu/lpswiki/index.php/Monty_Hall_problem

var skin = 'monobook';var stylepath = '/lpswiki/skins'; Trouble viewing the formulas? You need a MathML compatible browser. Monty Hall problem From LogicWiki Jump to: navigation search The Monty Hall Problem is a famous example of a problem that can be solved by Bayes' Theorem . It is another excellent example of Bayes' Theorem providing the correct, but counter-intuitive answer. Contents The Setup The Solution Understanding the Solution History ... edit The Setup The problem comes from the old TV Show "Let's Make a Deal," hosted by Monty Hall. You, the contestant, are presented with three doors labeled A, B and C. Behind one of those doors is a brand new car, while goats are behind the other two doors. The prizes are randomly distributed, and Monty knows what prize is behind what door. You choose a door (since they're all the same to you, let's pretend that you pick door A). Monty then opens up one of the two remaining doors, and then asks if you want to switch to the last remaining closed door. Monty will never open the door with a car behind it; the door he opens will have a goat behind it. So let's say that Monty opens door C (showing you a goat); he would then ask if you want to switch to door B or stay with door A. The question presented to you the contestant is: which choice gives you the best chance of winning the new car? Stay with A, or switch to B?

20. The Monty Hall Problem Web Page The Monty Hall Problem. The Monty Hall Problem gets its name from the TV game show, “Let’s Make A Deal,” hosted by Monty Hall 1. The scenario is such you are given the http://montyhallproblem.com/

The Monty Hall Problem The Monty Hall Problem gets its name from the TV game show, “Let’s Make A Deal,” hosted by Monty Hall . The scenario is such: you are given the opportunity to select one closed door of three, behind one of which there is a prize. The other two doors hide “goats” (or some other such “non–prize”), or nothing at all. Once you have made your selection, Monty Hall will open one of the remaining doors, revealing that it does not contain the prize . He then asks you if you would like to switch your selection to the other unopened door, or stay with your original choice. Here is the problem: Does it matter if you switch? This problem is quite interesting, because the answer is felt by most people—including mathematicians—to be counter–intuitive. For most, the “solution” is immediately obvious (they believe), and that is the end of it. But it’s not. Because most of the time, this “obvious” solution is incorrect. The correct solution is quite counterintuitive. Further, I’ve found that many persons have difficulty grasping the validity of the correct solution even after several explanations. Thus, this web page. Before I continue, you may wish to attempt to solve this problem by yourself. You’ve a good chance to do so, because you now know not to trust your instincts in this and that you should consider the problem very carefully. Try it.

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