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The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser 1st Edition

4.2 out of 5 stars 15 customer reviews
ISBN-13: 978-0195367898
ISBN-10: 0195367898
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Editorial Reviews

Review


"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


About the Author


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

  • Hardcover: 208 pages
  • Publisher: Oxford University Press; 1 edition (June 4, 2009)
  • Language: English
  • ISBN-10: 0195367898
  • ISBN-13: 978-0195367898
  • Product Dimensions: 9.2 x 0.8 x 6.3 inches
  • Shipping Weight: 12 ounces (View shipping rates and policies)
  • Average Customer Review: 4.2 out of 5 stars  See all reviews (15 customer reviews)
  • Amazon Best Sellers Rank: #658,181 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Rob Hardy HALL OF FAMETOP 1000 REVIEWER on June 14, 2009
Format: Hardcover
If you are old enough, you remember the sensation that the Rubik's Cube caused all the world over in 1980. No one is still alive that remembers the 1880 fad for the analogous two-dimensional "Fifteen Puzzle", which had fifteen numbered blocks within a four by four container and you were supposed to arrange them numerically. Mechanical puzzles can make storms like these, maybe because you can solve them over and over again, but it isn't often that word puzzles produce such fads. True, the Zebra Puzzle, a reasoning exercise consisting of fifteen seemingly unconnected statements that if regarded together the right way make a logical whole, was popular in 1962. Once you solved it, however, that was that. The Monty Hall Problem entered the public consciousness in 1990 and has been completely solved, but because the solution is so counterintuitive, it is still on the minds of many. One of those minds is that of Jason Rosenhouse, an associate professor of mathematics who has written _The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brain Teaser_ (Oxford University Press). "My original idea for this book," he writes, was that an entire first course in probability could be based on nothing more than variations of the Monty Hall problem." Indeed, some of the chapters here are full-power mathematics, with unknowns x, y, and z, summation or conditional probability symbols, and complicated equations choked with parentheses within brackets, and more. Math phobics won't get far with such stuff, but there is enough other material here, along with different explanations of the basic puzzle, that will be of interest to anyone who likes recreational mathematics in even the slightest degree.Read more ›
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Format: Hardcover
Believe it or not, this entire book is on the Monty Hall problem! The author, a mathematics professor, has analyzed this fascinating brain teaser from a variety of angles. After discussing the problem's history, he presents various attempts that have been made to understand it. The earlier attempts, including those by Marilyn vos Savant, tend to focus on logical arguments in order to arrive at the correct solution. But in order to solve the problem with mathematical rigour, the author uses some of the tools of his trade such as conditional probability and Bayes' Theorem. But that's not all. He also discusses a series of variants to the problem and proceeds to solve those as well. Finally, psychological and philosophical issues are also presented, partly in an attempt to understand why the human mind has been shown to have so much difficulty in solving this problem. The writing style is clear, friendly and authoritative, although some of the unfortunate editorial errors that the book contains may contribute towards slowing down a reader's attempts at following some of the author's arguments. Regarding accessibility, general readers can learn much from a good part of the main text because of the many clear explanations; however, several sections are fairly heavy with mathematics, a few of which can be rather challenging. Consequently, although anyone with an interest in this problem can benefit greatly from reading this book, math and science buffs are likely to glean the most out of it.
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Format: Hardcover Verified Purchase
The "Monty Hall Problem" by Jason Rosenhouse is currently the best coverage of this important problem.

He covers the version of the problem as it was made famous in Parade by vos Savant, and also it numerous variations and generalizations, its history, its occurrence in various fields (psychology, philosophy, quantum theory), and he gives a rather extensive bibliography which will be of great use to the serious student. The depth of coverage varies depending on the topic. For example, the classical analysis is satisfyingly extensive, while the fringe areas (quantum Monty Hall, for example) are just touched upon, and then references are given in the bibliography.

The chatty tone of the text is such that it probably should be categorized as a "mathematics for entertainment" book. And as such, Rosenhouse has allowed himself literary license that one might not normally expect in a math book. For example, we have to wait to until page 42 before "probability basics" are actually discussed . Douglas Adams allusions aside, it might have been better to have given at least the classical definition of probability somewhat earlier. The definition is further developed in pages 84 - 88 when he excellently discusses the classical, frequentist, and Bayesian concepts of probability. This section I consider one of the best in the book.

Rosenhouse states that the book should be within the reach of any undergraduate math major. This is probably overkill. If you know what a binomial coefficient is and what it is used for, know the classical definition of a probability in terms of a sample space, and know how to sum simple series, then you should have no difficulties.
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The writing is phenomenal - Rosenhouse tells a fun story. If you like to read stories about scientists, mathematicians, and old philosophical debates then this should be perfect for you.

I don't want to spoil this for you, so I'll step carefully here. Once you have seen the solution you'll probably realize that the answer is simple. But so many smart people continue fighting to be right even when the answer is simple and provable. I like to tell people about the Monty Hall problem and see what answer they come up with. And it's really fun to see how they're still baffled so often when you show them the answer. The best part is that some of the most befuddled people are the ones you'd think would already know.

If you haven't ever seen the solution before then Rosenhouse really should get the first crack at telling you, because he tells a great story. Unlike Malcolm Gladwell and the Freakonomics guys, he's telling the story of something that's truly counter-intuitive. And he does it very well.
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