The Monty Hall Problem A probability theory puzzle with solutions. English and German. http://www.remote.org/frederik/projects/ziege/
Extractions: [remote] [frederik] [projects] [monty hall] The following problem is taken from a quiz show on TV that really existed (or still exists). It is an interesting topic to discuss in almost any group of people because even the most intelligent often get into trouble, and is (in other languages) referred to as the Goat Problem. New: In compliance with the current domain grabbing hysteria, this page is now also available as http://www.ziegenproblem.de/, which is easier to memorize - at least for speakers of German. The quiz show candidate has mastered all the questions. Now it's all or nothing for one last time: He is lead to a room with three doors. Behind one of them there's an expensive sports car; behind the other two there's a goat. (Don't ask me why it's a goat. That's just the way it is.) The candidate chooses one of the doors. But it is not opened; the host (who knows the location of the sports car) opens one of the other doors instead and shows a goat. The rules of the game, which are known to all participants, require the host to do this irrespective of the candidate's initial choice. The candidate is now asked if he wants to stick with the door he chose originally or if he prefers to switch to the other remaining closed door. His goal is the sports car, of course!
Monty Hall Problem THE MONTY HALL PROBLEM. Throughout the many years of Let's Make A Deal 's popularity, mathematicians have been fascinated with the possibilities presented by the Three Doors http://www.letsmakeadeal.com/problem.htm
Extractions: THE MONTY HALL PROBLEM Throughout the many years of Let's Make A Deal 's popularity, mathematicians have been fascinated with the possibilities presented by the "Three Doors" ... and a mathematical urban legend has developed surrounding "The Monty Hall Problem." The CBS drama series featured the Monty Hall Problem in the final episode of its 2004-2005 season. The show's mathematician offered his own, very definite solution to the problem involving hidden cars and goats. The 2008 movie opens with an M.I.T. math professor (played by Kevin Spacey) using the Monty Hall Problem to explain mathematical theories to his students. His lecture also includes the popular "goats and cars behind three doors" example favored by many versions of the Problem. The London FINANCIAL TIMES published a column about the Monty Hall Problem on August 16, 2005, declaring positively that "the answer is, indeed, yes: you should change." However, the columnist, John Kay, notes that "Paul Erdos, the great mathematician, reputedly died still musing on the Monty Hall problem." The column resulted in several letters published on the "Leaders and Letters" page of the FINANCIAL TIMES on August 18 and 22 - and two follow-up columns by Mr. Kay on August 23 ( So you think you know the odds ) and August 31 ( The Monty Hall problem - a summing up ) in which he acknowledges that he received "a large correspondence on Monty Hall."
Monty Hall Dilemma For more on the controversy and its history please check the Monty Hall Problem article at the wikipedia. There are two simulations based on Marylin's interpretation. http://www.cut-the-knot.org/hall.shtml
Monty Hall Problem Web Sites Discourse on the Monty Hall Problem The following sites all pose the problem and discuss the solution and the conflict the solution has with our intuition. http://math.rice.edu/~pcmi/mathlinks/montyurl.html
Monty Hall Problem -- From Wolfram MathWorld The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is http://mathworld.wolfram.com/MontyHallProblem.html
Extractions: Monty Hall Problem The Monty Hall problem is named for its similarity to the Let's Make a Deal television game show hosted by Monty Hall. The problem is stated as follows. Assume that a room is equipped with three doors. Behind two are goats, and behind the third is a shiny new car. You are asked to pick a door, and will win whatever is behind it. Let's say you pick door 1. Before the door is opened, however, someone who knows what's behind the doors (Monty Hall) opens one of the other two doors, revealing a goat, and asks you if you wish to change your selection to the third door (i.e., the door which neither you picked nor he opened). The Monty Hall problem is deciding whether you do. The correct answer is that you do want to switch. If you do not switch, you have the expected 1/3 chance of winning the car, since no matter whether you initially picked the correct door, Monty will show you a door with a goat. But after Monty has eliminated one of the doors for you, you obviously do not improve your chances of winning to better than 1/3 by sticking with your original choice. If you now switch doors, however, there is a 2/3 chance you will win the car (counterintuitive though it seems). winning probability pick stick pick switch The Season 1 episode "
The Monty Hall Problem Statement of the Problem. The Monty Hall problem involves a classical game show situation and is named after Monty Hall, the longtime host of the TV game show Let's Make a Deal http://www.math.uah.edu/stat/games/MontyHall.xhtml
The Monty Hall Problem - Probability Puzzle The Monty Hall Problem is a famous probability puzzle. Ron Clarke takes you through the puzzle and explains the counterintuitive answer. http://www.flixxy.com/math-probability-puzzle.htm
Math Forum: Ask Dr. Math FAQ: The Monty Hall Problem In the threedoor problem, once you ve seen what s behind the second door is it better to stay with your first choice or switch doors? http://mathforum.org/dr/math/faq/faq.monty.hall.html
Extractions: For a review of basic concepts, see Introduction to Probability and Permutations and Combinations. Let's Make a Deal! Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? One way to think about this problem is to consider the sample space, which Monty alters by opening one of the doors that has a goat behind it. In doing so, he effectively removes one of the two losing doors from the sample space. We will assume that there is a winning door and that the two remaining doors, A and B, both have goats behind them. There are
The Monty Hall Page Let's Make a Deal Monty Knows Behind one of these doors is a car. Behind each of the other two doors is a goat. Click on the door that you think the car is behind. http://www.math.ucsd.edu/~crypto/Monty/monty.html
Extractions: Stuff I think about A new blog Mr Jenner on Channel 9 Reams and reams have been written about the Monty Hall problem, but no-one seems to have mentioned a simple fact which, once realised, makes the whole thing seem intuitive. 1/3: Couple picks correct door in the first place. If they change, they lose. 2/3: Couple picks the wrong door. The other wrong door is then eliminated, so if they change, they win. So changing has a 2/3 probablity of winning. This reasoning sounds like a more plausible argument for changing doors. probability depends on what you know . If you think about this for a while, it becomes obvious. A fair coin, when tossed, has a 50% probability of landing on heads. However, once the event has happened, the probablity collapses to 0% (if it landed tails up) or 100% (if it landed heads up). Let event A be the tossing of a coin at noon, and success defined by the coin landing heads up. At five seconds to noon the probability of success is 0.5. At five seconds past noon, when everybody can see that the coin landed heads up, the probability of success is 1.0. If the coin is tossed and it rolls under the sofa, then at five seconds past there is still a 50% chance of success. Although the coin has landed, no-one knows what the result is. Probability depends on what you know. If you know nothing about the coin, the probability of success is 0.5. Justin sent me this email: There are two doors, door #1 and door #2 behind which two real numbers are written at random. You get a prize if you choose the door with larger real number. At this point, the probability of winning a prize is 1/2. However, you get a chance. You first choose a door, and Monty shows you the number behind that door. What should you do in order to do better than 1/2? Or is it even possible to do better than 1/2?
The Monty Hall Page Let s Make a Deal Monty Knows Door 1 Door 2 Door 3. Behind one of these doors is a car. Behind each of the other two doors is a goat. http://math.ucsd.edu/~crypto/Monty/monty.html
Math Forum: Ask Dr. Math FAQ: The Monty Hall Problem In the threedoor problem, once you've seen what's behind the second door is it better to stay with your first choice or switch doors? http://mathforum.org/dr.math/faq/faq.monty.hall.html
Extractions: For a review of basic concepts, see Introduction to Probability and Permutations and Combinations. Let's Make a Deal! Imagine that the set of Monty Hall's game show Let's Make a Deal has three closed doors. Behind one of these doors is a car; behind the other two are goats. The contestant does not know where the car is, but Monty Hall does. The contestant picks a door and Monty opens one of the remaining doors, one he knows doesn't hide the car. If the contestant has already chosen the correct door, Monty is equally likely to open either of the two remaining doors. After Monty has shown a goat behind the door that he opens, the contestant is always given the option to switch doors. What is the probability of winning the car if she stays with her first choice? What if she decides to switch? One way to think about this problem is to consider the sample space, which Monty alters by opening one of the doors that has a goat behind it. In doing so, he effectively removes one of the two losing doors from the sample space. We will assume that there is a winning door and that the two remaining doors, A and B, both have goats behind them. There are
Andrew Graham | Monty Hall Simulation of the 3-door problem in Flash, along with a brief discussion. http://www.andrewgraham.co.uk/flash/montyhall
Extractions: Picture the scene. You've made it through to the final round of a game show. There are three doors in front of you. Behind one of the doors is the star prize - a brand new car. There is a goat behind each of the other two doors. You make your choice, hoping to select the star prize. The game show host (who knows where the car is hidden) opens a different door to reveal a goat. The choice is now down to two doors. He asks whether you'd like to stick with your original choice or whether you'd like to switch doors... It is easy to assume that there is a fifty-fifty chance of picking the correct door first time round. In fact you are twice as likely to choose the car if you switch doors! It's hard to believe, isn't it? After all, when the host opens one door there's a straight choice between two doors - one hiding a goat, the other the car. The argument that there's a fifty-fifty chance of winning is a very seductive one - but it's wrong.
U Of T Mathematics Network -- Problems And Puzzles Includes interactive games, problems and puzzles including the Monty Hall Problem and the Tower of Hanoi and questions pages with answers and discussion. http://www.math.toronto.edu/mathnet/probpuzz.html
Extractions: Go to University of Toronto Mathematics Network Home Page You can select any of the items below: Try your hand at these problems, and mail in your answers! If your interest is in recreational mathematics, try playing these games, then figuring out the mathematics behind them. The following sites are not part of the University of Toronto Mathematics Network, but since there are already many good traditional-style problems available on the Internet, we decided we'd just point you to them, while we spend more time developing the interactive projects and activities unique to this site. A good, comprehensive source of many mathematical materials. Not a problem collection, but a newsletter chock full of puzzles, trivia, humour, and even some real mathematics. Published by undergraduate mathematicians at the University of Toronto. This page last updated: September 27, 1999
Cognitive Dissonance In Monkeys - The Monty Hall Problem - New Apr 8, 2008 Some experiments that purport to show cognitivedissonance effects might be explainable by statistics alone. http://www.nytimes.com/2008/04/08/science/08tier.html?ei=5090&en=dc270baec0c
Monty Hall - Wikipedia, The Free Encyclopedia During the week of March 22, 2010, Hall hosted several segments of the Deal alongside Brady. The program has been renewed for the 20102011 season. The Monty Hall Problem http://en.wikipedia.org/wiki/Monty_Hall
Extractions: Winnipeg Manitoba Canada Occupation Game show host, actor, producer, singer, sportscaster Years active 1953–present Spouse Marilyn Hall (1947-present) Monte Halperin OC OM (born August 25, 1921), better known by the stage name Monty Hall , is a Canadian -born MC producer actor singer and sportscaster , best known as host of the television game show Let's Make a Deal The handprints of Hall in front of Hollywood Hills Amphitheater at Walt Disney World 's Disney's Hollywood Studios theme park. Hall was born in Winnipeg Manitoba Canada , the son of Rose (née Rusen) and Maurice Harvey Halperin, both of whom belonged to an Orthodox congregation of Judaism and who jointly owned a slaughterhouse. He was raised in Winnipeg's north end, where he attended St. John's High School . Hall started his career in Toronto in radio. Early in his career, Hall hosted game shows such as
Analysis Of The Monty Hall Problem There are numerous web pages devoted to discussion and analysis of the Monty Hall problem. I hope to add something new and interesting to the discussion with an analysis http://kevingong.com/Math/MontyHall.html
Extractions: Kevin's Home Page Kevin Gong March 17th, 2003 There are numerous web pages devoted to discussion and analysis of the Monty Hall problem. I hope to add something new and interesting to the discussion with an analysis of a more interesting problem. For those of you living in a mathematical cave, I'll briefly explain the problem and very little on the controversy. In 1991, Parade Magazine published a column "Ask Marilyn" in which Marilyn vos Savant replies to a reader's question: "Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the other doors, opens another door, say No. 3, which has a goat. He then says to you, 'Do you want to pick door No. 2?' Is it to your advantage to take the switch?" Marilyn replied that the answer was yes, and there was a big uproar and mathematicians from across the country attacked her. I'll spare you the details. You can do a web search on that if you're interested. I'm more interested in the mathematics.
