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1. Notes: The Monty Hall Problem
The monty hall problem. Jason linked The monty hall problem in his remainderedlinks, and it reminded me that I made a web version of the problem for kicks.
http://notes.torrez.org/2004/04/the_monty_hall_.html

2. Marilyn Is Tricked By A Game Show Host
Which means, of course, that the only person who can answer this versionof the monty hall problem is Monty Hall himself. Here is
http://www.wiskit.com/marilyn.gameshow.html

3. The Monty Hall Problem
Dr. Ray Cafolla s Class Pages. The monty hall problem. Statement of theProblem. Write a program in C++ to simulate the monty hall problem.
http://cyberlearn.fau.edu/cafolla/courses/cpp/montyhall.htm

Extractions: Class Pages The Monty Hall Problem The Monty Hall problem involves a classical game show situation and is named, of course, after Monty Hall , the long-time host of the show Let's Make a Deal . There are three doors labeled 1, 2, and 3. A car is behind one of the doors, while goats are behind the other two: The rules are as follows: The player selects a door. The host selects a different door and opens it. The host gives the player the option of switching from her original choice to the remaining closed door. The door finally selected by the player is opened and she either wins or loses. The Monty Hall problem became the subject of intense controversy because of several articles by Marilyn Vos Savant in the Ask Marilyn column of Parade magazine, a popular Sunday newspaper supplement. The controversy began when a reader posed the problem in the following way: Suppose you're on a game show, and you're given a choice of three doors. Behind one door is a car; behind the others, goats. You pick a doorsay No. 1and the host, who knows what's behind the doors, opens another doorsay No. 3which 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? Marilyn's response was that the contestant should switch doors, claiming that there is a 1/3 chance that the car is behind door 1, while there is a 2/3 chance that the car is behind door 2. In two follow-up columns, Marilyn printed a number of responses, some from academics, most of whom claimed in angry or sarcastic tones that she was wrong and that there are equal chances that the car is behind doors 1 or 2. Marilyn stood by her original answer and offered additional, but non-mathematical, arguments.

4. The Monty Hall Problem - A State-space Explanation
The monty hall problem a state-space explanation. Here is yet another explanationof the answer. Notes A friend called to ask about the monty hall problem.
http://www.vendian.org/mncharity/dir2/montyhall/

Extractions: so we tell "Monty" we've switched our choice to green Comments encouraged. Mitchell N Charity mcharity@lcs.mit.edu Notes: A friend called to ask about the Monty Hall Problem. I liked this explanation, but it didn't work over the phone. Not seeing it already online, I wrote this. This presentation is similar to this Answer to the Monty Hall Problem , but sufficiently different that I went ahead with this one anyway. Doables: History: 1998.Oct.15 Created.

5. Monty Hall Problem :: Online Encyclopedia :: Information Genius
monty hall problem. Online See Empirical proof of the monty hall problemfor a Perl program which demonstrates the result. Variants. In
http://www.informationgenius.com/encyclopedia/m/mo/monty_hall_problem.html

Extractions: 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

6. The Monty Hall Problem
The monty hall problem. (This is similar to the routine on the TV game showLet s Make a Deal, hosted by Monty Hall, hence the name of the problem.).
http://www.camosun.bc.ca/~jbritton/montyhall/jbmontyhall.htm

Extractions: Suppose you're on a game show and you're given the choice of three doors. Behind one door is the grand prize; behind the others, booby prizes. You pick a door, say Door 1, and the host, who knows what is behind each door, opens another door, say Door 2, revealing a booby prize. The host then offers you the opportunity to change your selection to Door 3. Should you stick with your original choice or switch? Does it make any difference? (This is similar to the routine on the TV game show Let's Make a Deal , hosted by Monty Hall, hence the name of the problem.) Assuming that the host always chooses to open a door with a booby prize, and would never reveal the grand prize, the possibly surprising answer is that you should switch to the third door, which is now twice as likely as your original choice to be hiding the grand prize. When you chose Door 1, the probability that you chose the grand prize was 1/3 and the probability that it was behind one of the other doors was 2/3. By showing you which of Doors 2 and 3 does not hide the grand prize (Door 2, say), the host is giving you quite a bit of information about those two doors. The probability is still 2/3 that one of them hides the grand prize, but now you know which of the two it would be: Door 3. So, the probability is still only 1/3 that the grand prize is behind Door A, but 2/3 that it is behind Door 3. If you find this result counterintuitive (and even most mathematicians do) and your browser is JAVA-capable, try the simulation below. Choose a door by clicking on it. The host (your computer) will then open one of the other doors, revealing a pig. You may then, by clicking on the appropriate door, choose to stick with your choice or switch to the remaining door. After a moment the doors will close to allow you to try again. Below the doors are shown two running calculations: the experimental probability that you will win if you stay with your original choice and the experimental probability that you will win if you switch. After many tries, will these numbers be close to 1/2, or will they be close to 1/3 and 2/3 respectively?

7. Harry S Monty Hall Page
The monty hall problem is one that comes up fairly regularly in alt.folklore.urban,and it is one that people consistently have problems understanding, hence
http://www.het3.com/monty-main.html

Extractions: Harry's Monty Hall Page The Monty Hall Problem is one that comes up fairly regularly in alt.folklore.urban, and it is one that people consistently have problems understanding, hence it is only reasonable to have a sort of FAQ for it. This FAQ is organized thusly: Part 1: The Monty Hall Problem itself, and the Answer Part 2: Compelling Explanations of the Answer Part 3: Common Misconstructions of the Problem, and their Rebuttals Part 1: The Monty Hall Problem, and the Answer You are a guest on Let's Make a Deal , hosted by Monty Hall. He presents you with three doors, behind one of which is a Brand! New! Car! and behind the other two are goats. You are given one guess as to which door has the car. Monty then opens one of the other doors to show you a goat, and you are given the opportunity to switch to the other unopened door. Should you switch, or should you stay with your initial guess? Note: There are certain assumptions in the problem that are important to understand. One is that Monty is honest, and always behaves the same way. This means that you are always provided the choice to switch, which is apparently not the case on the actual Let's Make a Deal show, and that Monty's subsequent behavior does not change relative to whether you initially picked the winning door. This is a problem about probability analysis, not about realistically modeling the behavior of a game show host. And the answer is... yes, you should switch. Your odds of winning increase to 2:1 if you switch, and remain at 1:2 if you do not.

8. Gregor's World: The Full Monty (Hall Problem)
The Full Monty (Hall Problem). It is very easy to get the wrong answer to Themonty hall problem. The monty hall problem is deciding whether you do.
http://www.gregorpurdy.com/gregor/gw/by-entry/000526.html

Extractions: Main It is very easy to get the wrong answer to The Monty Hall Problem . I'll quote an excerpt of the above referenced page at MathWorld without spoilers so you can have the fun of trying to spot the error as you follow along: 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. Here is my exploration of why it is so easy to get wrong. When presented with a small enough problem (or one that can be reduced to a small enough problem), exhaustion of cases is a great way to search for a solution. Lets apply this technique to the Monty Hall Problem...

9. The Monty Hall Problem
. Welcome to the probability problemthat has vexed many a person over many a year. Rumours aboutThe monty hall problem.
http://people.bu.edu/trachten/java_stuff/monty.html

Extractions: Welcome to the probability problem that has vexed many a person over many a year. Rumours about this problem have flown far and wide, the most egregious being that the wrong answer was once published in a journal. When the woman with the highest known IQ (at the time) wrote in with a correction, her correction was refused because it is quite counter-intuitive. I, myself, have seen professors of mathematics run computer simulations because they did not believe the theoretical result. The question is simple: there are three doors, with the prize of your dreams behind one of them (use your imagination). You select one door, and the host decides he's going to be nice to you; he shows you which of the other doors definitely does not contain the prize. Your task now is to decide: do you stick with your choice, or do you change your mind and opt for the one remaining closed door.

10. The Monty Hall Problem
The monty hall problem. You are a player on a gameshow. Before you are three doors,behind each is either a goat or a car. There are two goats and one car.
http://www.interfootball.co.uk/monty/default.htm

Extractions: Interfootball Problem Mate Monty Hall Big Chain Report It Get a Date The Monty Hall Problem You are a player on a gameshow. Before you are three doors, behind each is either a goat or a car. There are two goats and one car. Select a door and one of the remaining doors will open to reveal a goat. Click on door Statistics (0) If Stuck If Changed Overall Did Stick Did Change Home Interfootball Problem Mate Monty Hall Big Chain Report It Get a Date Contact pw@interfootball.co.uk

11. No. 1577: The Monty Hall Problem
No. 1577 THE monty hall problem. by John H. Lienhard. I ve been running intothe monty hall problem lately. I suspect that many of you know about it.
http://www.uh.edu/engines/epi1577.htm

Extractions: THE MONTY HALL PROBLEM by John H. Lienhard Click here for audio of Episode 1577. Today, we learn not to turn our back on information. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. I' ve been running into the Monty Hall Problem lately. I suspect that many of you know about it. It came to my attention the other day when I ran into a colleague from the math department. She told me about it and left me scoffing in disbelief. I should've known about the problem, since it goes back to the old TV show, Let's Make a Deal . Host Monty Hall would offer a contestant three doors. One had a prize behind it. If the contestant guessed the correct door, he would win the prize. But, before the door that he chose was opened, Monty Hall (who knew where the prize was) would say, "Of the two remaining doors, I'll open this one, which has no prize behind it." Then Hall would add, "Now, would you like to change your guess?" The contestant could either decide that the first guess was correct or switch to the other unopened door. "The contestant should switch," said my mathematician friend. "Why?" I asked. "Because the probability of getting the prize will rise from one chance in three to two out of three."

12. The Monty Hall Problem
The monty hall problem. This problem has rapidly become part of themathematical folklore. The American Mathematical Monthly, in
http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node32.html

Extractions: Next: Master Mind Up: Mathematical Games Previous: Mathematical Games This problem has rapidly become part of the mathematical folklore. The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article. Problem: A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car? If the host always opens one of the two other doors, you should switch. Notice that of the time you choose the right door (i.e. the one with the car) and switching is wrong, while of the time you choose the wrong door and switching gets you the car. Thus the expected return of switching is which improves over your original expected gain of Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.

13. The Monty Hall Problem
Previous Mathematical Games. The monty hall problem. This problemhas rapidly become part of the mathematical folklore. The American
http://db.uwaterloo.ca/~alopez-o/math-faq/node65.html

Extractions: Next: Master Mind Up: Mathematical Games Previous: Mathematical Games This problem has rapidly become part of the mathematical folklore. The American Mathematical Monthly, in its issue of January 1992, explains this problem carefully. The following are excerpted from that article. Problem: A TV host shows you three numbered doors (all three equally likely), one hiding a car and the other two hiding goats. You get to pick a door, winning whatever is behind it. Regardless of the door you choose, the host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Does switching increases your chances of winning the car? If the host always opens one of the two other doors, you should switch. Notice that 1/3 of the time you choose the right door (i.e. the one with the car) and switching is wrong, while 2/3 of the time you choose the wrong door and switching gets you the car. Thus the expected return of switching is 2/3 which improves over your original expected gain of 1/3. Even if the hosts offers you to switch only part of the time, it pays to switch. Only in the case where we assume a malicious host (i.e. a host who entices you to switch based in the knowledge that you have the right door) would it pay not to switch.

14. Das Monty Hall Problem Oder Das Ziegenproblem
monty hall problem ,
http://www.grg19bi73.asn-wien.ac.at/~bica/montyhall/monty.html

15. The Monty Hall Problem
Home July 1997 - monty hall problem. The monty hall problem. MontyHall This has come to be known as the monty hall problem. It is
http://www.visi.com/~sgrantz/july/monty.html

Extractions: Home July 1997 -> Monty Hall Problem Monty Hall hosted a game show around 25 years ago in which he fast-talked people into making deals for cash and prizes. Audience members wore ridiculous costumes, and at the end of the show, Monty would wander through the melange of clowns, chickens, and chefs, offering quick cash if selected people could produce a desired item. "I'll give you \$40 if you have hairspray in your purse," Monty would ask some woman in a green bodysuit with foam flower petals surrounding her head. It was a laugh riot. The centerpiece of the show, however, was "The Deal". Monty would pick someone from the audience, give them cash, the tell them that behind one of three doors was a lovely gift. They could keep the cash, or pick one of the doors. After picking, say, door #1, the real fun began. Without opening door #1, Monty would reveal the contents of door two, usually a lovely Amana kitchen appliance. Then he would ask if they wanted to switch from door #1, contents unknown, to the remaining door, #3. This has come to be known as the Monty Hall Problem. It is very well known in mathematical and statistical circles because the correct answer to the problem is counterintuitive. You should always switch.

16. Magpie B.: The Monty Hall Problem
May 05, 2004. The monty hall problem. montyI am part of a team that is writinga guide to help middle school math teachers brush up on their math.

17. The Monty Hall Problem
The monty hall problem. The following problem is taken from a quiz showon TV that really existed (or still exists). It is an interesting
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!

18. Mudd Math Fun Facts: Monty Hall Problem
19992003 Francis Edward Su. From the Fun Fact files, here is a FunFact at the Medium level monty hall problem. Figure 1 Figure 1.
http://www.math.hmc.edu/funfacts/ffiles/20002.6.shtml

Extractions: Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Medium level: Figure 1 Here's a problem that makes the round every few years, and each time, it is hotly debated. You are on a game show. You are presented with a choice of 3 doors: behind one is a luxury car, and behind the other two are nothing. The host asks you pick one of the doors. After you do this, as part of the game he opens one unpicked doors which he knows is empty. There are now only the door you picked and one remaining door which are unopened. You are asked if you would like to switch your choice. Should you switch? Presentation Suggestions:

19. Monty Hall
CONCLUSION As for the correct solution to the monty hall problem, it reallydepends on one s interpretation of the way the game show is run.
http://barryispuzzled.com/zmonty.htm

Extractions: A classic probability teaser In September 1990, Marilyn vos Savant, puzzle columnist for the U.S. magazine Parade, was sent a probability teaser by a reader. Its publication in her "Ask Marilyn" column together with her solution has produced much debate amongst mathematicians and laymen alike ever since. Apart from it's challenge to common intuition, one reason it has attracted so much interest is that Ms von Savant is listed in the Guinness Book of World Records as having the highest recorded score in an IQ test (228 : based on a score attained at 10 years old) and that proving her wrong, some respondents no doubt reasoned, might indicate that they too were blessed with such uncommon prowess. To date, Ms vos Savant has received over 10,000 letters on the puzzle, mostly disagreeable, and articles are still being written claiming new insights that show where Ms vos Savant got it wrong. The present article argues that the solution really depends on one's interpretation of the stated problem. One of the earliest known appearances of the problem was in Joseph Bertrand's Calcul des probabilites (1889) where it was known as Bertrand's Box Paradox. It later reappeared in Martin Gardner's 1961 book

20. The Monty Hall Problem
the monty hall problem. Should you switch? This problem was never on Let s Makea Deal , of course, but it was Monty Hall s show that inspired the problem.
http://www.andrew.cmu.edu/user/nal/monty_hall_problem.htm

Extractions: Here's the situation: You are a contestant on Monty Hall's "Let's Make a Deal". Monty shows you three doors and tells you that behind one of them is a new car and behind the other two are goats. He asks you to pick a door, any door. Once you make your choice, he opens one of the other two doors and shows you a goat because he knows where the prize is hidden. Then, he asks if you would like to keep your original choice or switch to the remaining door. Should you switch? This problem was never on "Let's Make a Deal", of course, but it was Monty Hall's show that inspired the problem. It seems to have originated in Scientific American in 1959. The author, Martin Gardner, called it a "wonderfully confusing little problem." He could not have known that his observation stating that "in no other branch of mathematics is it so easy for experts to blunder as in probability theory" would be proven true so many times. In 1976, it appeared again in American Statistician . It was further analyzed in 1986 in the Journal of the American Mathematical Society . Finally, the most famous analysis of the Monty Hall Problem came on September 9, 1990, when Marilyn vos Savant "answered" the question in her column in "Parade" magazine. Surprisingly, she got it wrong, sparking a controversy that swept the country. Countless mathematicians and statisticians have incorrectly answered the problem

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