The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser [NOOK Book]

Overview

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host—call him Monty Hall—opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse ...

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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser

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Overview

Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host—call him Monty Hall—opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.

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Editorial Reviews

From the Publisher
"Excellent survey...If one wants to see "The Full Monty," this is definitely the book to buy. Highly recommended." — Choice

"Those intrigued by the original Monty Hall problem will find that this book is a superb source of variants of the problem, pays careful attention to the hidden assumptions behind the problems, and is written in a witty accessible style that never lapses into flippancy. This is a model of how to accessibly introduce mathematical material at an elementary level that is not a mere popularization of the material. A virtue of the book is that it goes beyond mere exposition to make some serious contributions to the discussion, including a proof that the strategy of switching at the last minute in the progressive version is uniquely optimal and a discussion of some philosophical treatments on the topic."—Mathematical Reviews

"...a masterful job of tracing the problem back to its origin...much more comprehensive and wide-ranging than the many articles on the subject that have dribbled out...Rosenhouse offers readers much to think about concerning the perplexing question of whether to stick or switch." -Science

"Rosenhouse is both entertaining and precise in his writing. He carefully makes the point that conditional probability is difficult to intuitively process, often because what is being conditioned on is not clear. The book is both informative and an entertaining journey for both those schooled in probability and those with little background in probability."—The American Statistician

"Overall, this book is an excellent example of how a problem that is understandable by all can be used to introduce key concepts in mathematics and probability. If you are already familiar with the problem, this book will make you think more deeply about the nature of chance, and what Rosenhouse describes as "the perils of intuition". If Monty Hall is new to you, then you have a choice: stick or switch? You may be surprised." — Tom Fanshawe, Lancaster

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Product Details

  • ISBN-13: 9780199887927
  • Publisher: Oxford University Press, USA
  • Publication date: 5/4/2009
  • Sold by: Barnes & Noble
  • Format: eBook
  • Sales rank: 924,754
  • File size: 19 MB
  • Note: This product may take a few minutes to download.

Meet the Author

Jason Rosenhouse is an Associate Professor of Mathematics at James Madison University in Virginia.

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Sort by: Showing 1 Customer Reviews
  • Posted May 2, 2009

    more from this reviewer

    A truly comprehensive account - and surprsingly comprehensible!

    What's in this book?

    It's about the Monty Hall problem, the classic version of which is:


    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.

    You are then offered a chance to change doors, or stick with your
    choice.

    What should you do?


    Here's the table of contents:
    1. Ancestral Monty
    has considerable detail about the origins of the problem and the huge outcry when vos Savant published the right answer. This is presented in a light and humorous way, showing how the intuition of many people is completely wrong.

    2. Classical Monty
    covers the problem above, giving reasons based on intuition, as well as on formal probability.


    3. Bayesian Monty
    covers a variation in which Monty does not know which door has the car, and introduces Bayesian notions.

    4. Progressive Monty
    is by far the most technical in the book; it covers many variations on the problem, and teaches a lot of probability theory.

    5. Miscellaneous Monty
    covers some additional variations on the problem

    6. Cognitive Monty
    discusses why our intuition is so wrong on this problem and others, and reviews research into this.

    7. Philosophical Monty
    discusses philosophical issues in probability

    8. Final Monty
    sums up.
    Who should read the book?

    I think it has a couple audiences. First, if you are taking a formal probability course at university, this could be a good backup to your text. OTOH, if you are *teaching* such a course, you could use this as a main text (I've never seen a probability text that is this much fun to read). A course based on this book would cover a lot of the ground of a one-semester intro to probability course.

    Among the general population, I think this book could be read in two ways: First, you could read chapters 1, 2, 6, 7, and 8, and either skip 3, 4, and 5 or skim them. (Chapter 4, in particular, will be heavy going). Second, if you want to learn probability theory, you could read the whole book. In this case, you'll want to read it more like a text book.

    1 out of 1 people found this review helpful.

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