Geometry.Net - Theorems_And_Conjectures: Monty Hall Problem

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

Extractions: Login Posted by John Marden , 2/28/00 at 1:46:25 PM. 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 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): 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
Eric's Monty Hall Three-Door Problem Page
monty hall ThreeDoor problem. The monty hall three-door problemasks a contestant to choose one of three doors, hoping to find
http://www.mv.com/ipusers/arcade/monty.htm

Extractions: Other pages: Eric Postpischil's Home Page Coin Flips Dice Springs and Ropes ... Math Quotes The "Monty Hall" three-door problem asks a contestant to choose one of three doors, hoping to find the one door that conceals a prize. The other two doors conceal duds. After the contestant chooses, Monty Hall (the master of ceremonies of the Let's Make a Deal television show) opens one of the doors the player did not choose to reveal a dud. (It is important that Monty Hall always intentionally opens a door with a dud. This is not always made clear in statements of the problem.) Then the contestant is permitted to stay with their original choice or switch to the other unopened door. The question is, what is the player's probability of getting the prize if they switch? Here is the source code for a C program to simulate the problem. You may wish to have your browser save the file to disk rather than displaying it. The problem may also be phrased in terms of selecting one red card from three cards, the other two of which are black. Here is an explanation of why switching yields the red card two-thirds of the time: Imagine three thousand card tables. On each of the tables, a dealer has randomly arranged one red card and two black cards, face down. At each table, you randomly put a marker labeled "1" on one of the cards, representing your first choice.
Daily Trivia
"); } // Remember the age old game show, "Let's Make A Deal " with monty hall and Carol Merrill? Well, a couple of months ago, we posed a little puzzler inspired by said game show. The puzzler involved switching boxes and changing the odds of
http://cartalk.cars.com/About/Monty

Extractions: Remember the age old game show, "Let's Make A Deal," with Monty Hall and Carol Merrill? Well, a couple of months ago, we posed a little puzzler inspired by said game show. The puzzler involved switching boxes and changing the odds of winning the big prize. And boy, did it cause an uproar! We practically started World War III. The puzzler itself was pretty straightforward. When we gave our answer that switching would increase your odds of winning big, all Hell broke loose. We got satchels full of mailmuch of it on letterhead from prestigious universities, with inscriptions like, "The Josiah Wadsworth Endowed Professorship of Statistical Phenomenology, Department of Applied Mathematics, Somewhat Prestigious University." Many of the letters were vituperative... and some were even downright nasty. We got mail that told us we were wrong headed, mail that told us in exactly which wrong place our heads must be, and mail telling us where we could put our heads, provided they weren't there already. Well, now we're here to prove that we're right. Why go through all this trouble? Because what could be more fun than proving a bunch of pompous academics wrong!!
Monty Hall, 3 Doors
Follow this link to the multiple trials applet Please help us by suggesting enhancements or reporting bugs in this program. Or, send us other questions or comments about this activity. © Copyright 19972002 The Shodor Education Foundation, Inc.
http://www.shodor.org/interactivate/activities/monty3
The Monty Hall Page
Play the Game An Explanation of the game. Back Home Programs Documentation Internet People.
http://math.ucsd.edu/~crypto/Monty/Montytitle.html
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
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

Extractions: 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.

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