21. The Monty Hall Problem A probability theory puzzle with solutions. English and German. http://www.remote.org/frederik/projects/ziege/

[remote] [frederik] [projects] [monty hall] The Monty Hall Problem 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 Scenario 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!

22. 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

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."

23. 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

24. 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

The WWW Tackles The Monty Hall Problem 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. Monty Hall, Let's Make a Deal, Problem http://www.nadn.navy.mil/MathDept/courses/sm230/montyhal.htm The Infamous Monty Hall Problem http://www.comedia.com/Hot/monty.html ... http://www.wiskit.com/marilyn.gameshow.html Simulations of the Monty Hall Problem: Three Door Puzzle A great site! The problem is meticulously posed, the graphics are excellent and it is fun to "play". The is a full explaination of the solution and nice generalization of the problem for n doors. http://www.intergalact.com/threedoor/threedoor.html Education, Mathematics, Fun, Monty Hall Dilemma Another great site. Details of the "Ask Marilyn" controversy and a cool simulation. http://mars.superlink.net/user/abogom/hall.html Computer Generated Random Numbers A thorough discussion on computer generated random numbers. Follow the link for the Monty Hall simulation (which uses random numbers). http://mindvox.phantom.com/~dsharp/rn.html

25. 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

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Interactive Demonstrations 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 "

26. 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

27. 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

28. The Infamous Monty Hall Problem Short introduction for beginners. http://www.comedia.com/hot/monty.html

The Infamous Monty Hall Problem The Setup you are presented with 3 doors (A, B, C) only one of which has something valuable to you behind it (the others are bogus) you do not know what is behind any of the doors You choose a door Monty then counters by showing you what is behind one of the other doors (which is a bogus prize), and asks you if you would like to stick with the door you have, or switch to the other unknown door The question is should you switch? Another question is Does it matter? The answer lies behind this link Don't look until you've decided upon your answer. Home Broadcatch Technologies CoMedia Consulting Words ... Hot List This page maintained by CoMedia Consulting webmaster@CoMedia.com Last modified: Fri Aug 30 13:51:58 PDT 1996

29. 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

Ask Dr. Math: FAQ The Monty Hall Problem Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home 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

30. 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

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. OR Click here to play the NEW Monty Does Not Know version of the game! OR Click here for an explanation of the game Back Home Programs ... People

31. A New Approach To The Monty Hall Problem « Reenigne Blog Introduces the problem and tries to look at the problem in a new light. http://www.reenigne.org/blog/montyhall/

Reenigne blog Stuff I think about A new blog Mr Jenner on Channel 9 A new approach to the Monty Hall problem 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. Addendum 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?

32. 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

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. OR Click here to play the NEW Monty Does Not Know version of the game! OR Click here for an explanation of the game Back Home Programs ... People

33. 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

Ask Dr. Math: FAQ The Monty Hall Problem Dr. Math FAQ Classic Problems Formulas Search Dr. Math ... Dr. Math Home 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

34. Andrew Graham | Monty Hall Simulation of the 3-door problem in Flash, along with a brief discussion. http://www.andrewgraham.co.uk/flash/montyhall

home flash typefaces sites ... contact Monty Hall 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. The problem is based on a real-life scenario from the American TV gameshow Let's Make a Deal and gets its name from the show's host. The problem gained notoriety when it became the subject of the syndicated American newspaper column

35. Pigeons Beat Humans At Solving 'Monty Hall' Problem | LiveScience Pigeons outdid people in solving the Monty Hall problem from http://www.livescience.com/animals/pigeons-monty-hall-problem-100304.html

36. 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

Navigation Panel: Go backward to Interactive Activities and Games Go forward to Questions and Discussion Switch to text-only version (no graphics) Go to University of Toronto Mathematics Network Home Page Problems and Puzzles You can select any of the items below: International Mathematical Talent Search Problems Try your hand at these problems, and mail in your answers! Interesting Mathematical Games 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. The Math Forum A good, comprehensive source of many mathematical materials. MAT 007 I News 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

37. 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

38. 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

Monty Hall From Wikipedia, the free encyclopedia Jump to: navigation search Monty Hall Born Monte Halperin August 25, 1921 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 Contents Life and career Entry into the United States Let's Make a Deal Other game show work ... edit Life and career 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

39. Monty Hall Problem Applet - Jupiterinc.net This site may harm your computer. http://jupiterinc.net/VXXojHP/

40. 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

Kevin's Math Page Home Contact Home Research ... Contact Topics: Polyominoes Egyptian Fractions Graceful Graphs 16 Puzzle ... How To Become A Millionaire search by FreeFind Polyominoes Home Kevin's Math Blog Kevin's Home Page Analysis of the Monty Hall Problem 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.

Page 2     21-40 of 84    Back | 1  | 2  | 3  | 4  | 5  | Next 20