Classic Problems of Probability 1st Edition by Prakash Gorroochurn (PDF)

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Winner of the 2012 PROSE Award for Mathematics from The American Publishers Awards for Professional and Scholarly Excellence.”A great book, one that I will certainly add to my personal library.” —Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New HampshireClassic Problems of Probability presents a lively account of the most intriguing aspects of statistics. The book features a large collection of more than thirty classic probability problems which have been carefully selected for their interesting history, the way they have shaped the field, and their counterintuitive nature.From Cardano’s 1564 Games of Chance to Jacob Bernoulli’s 1713 Golden Theorem to Parrondo’s 1996 Perplexing Paradox, the book clearly outlines the puzzles and problems of probability, interweaving the discussion with rich historical detail and the story of how the mathematicians involved arrived at their solutions. Each problem is given an in-depth treatment, including detailed and rigorous mathematical proofs as needed. Some of the fascinating topics discussed by the author include:Buffon’s Needle problem and its ingenious treatment by Joseph Barbier, culminating into a discussion of invarianceVarious paradoxes raised by Joseph BertrandClassic problems in decision theory, including Pascal’s Wager, Kraitchik’s Neckties, and Newcomb’s problemThe Bayesian paradigm and various philosophies of probabilityCoverage of both elementary and more complex problems, including the Chevalier de Méré problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradoxClassic Problems of Probability is an eye-opening, one-of-a-kind reference for researchers and professionals interested in the history of probability and the varied problem-solving strategies employed throughout the ages. The book also serves as an insightful supplement for courses on mathematical probability and introductory probability and statistics at the undergraduate level.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐As the title implies, Dr. Gorroochum takes us through historical, probabilistic problems, along with their mathematical solutions. The problems are arranged chronologically and it gives the reader a strong sense of how recently humanity had only a limited ability to conceptualize and predict something as simple as rolling dice. Each classical problem is accompanied with an historical vignette, which is always fascinating and usually includes gems like, “so he wrote a letter to Sir. Isaac Newton.”The vignettes serve not only as an historical story, but also to teach the reader about probability, as it was discovered. However, if this is not in the interest of a reader, it is also easy to enjoy the book as a collection of fascinating historical stories. The vignettes teach probability in a different way one would learn it in a classroom setting. Instead of learning the ‘rule’, the reader learns a series of problems that are sometimes solved with discrete, problem-specific solutions. It forced me to reflect on modern-day scientific (not just statistical) problems and gave me a different perspective on modern day research.Overall, this is a very well written and fascinating book. I highly recommend it to anyone who is interested in statistics, probability or intellectual history.

⭐As advertised, perfect condition.

⭐This book contains 33 brief (mostly 5-12 pages) chapters, each dealing with one “classic” mathematical question, giving the original author’s treatment as well as discussion by subsequent writers and the present author. The first half proceeds from Cardano and games of chance (1564) to the Buffon needle problem (1777), and the second half from Bertrand’s ballot problem (1887) to Parrondo’s paradox (1996). So it’s snapshots from the history of mathematical probability, emphasizing the detailed mathematics of the specific problems rather than any broader theme. Typical textbooks give only brief historical asides, and only a minority of mathematicians bother with detailed serious history of the subject. So this book usefully fills a niche, by collecting this material together in one place, and it should be commended as a scholarly expository achievement.It is written for people who want to see the mathematics, so requires the reader to have taken a fairly serious introductory course in mathematical probability, but for such an audience it is clearly written. A quick comparison with some Wikipedia entries shows this book to be generally more authoritative, though to my taste the Wikipedia discussion of Benford’s law is more illuminating.My one quibble concerns Parrondo’s paradox. The mathematics of this counter-intuitive result are explained well. However, the author (like many other authors) summarizes the result as “by random playing two losing games, the player comes out a winner!”. This is very misleading, because it has been known since the 1950s that the right mathematical formalization of the intuitive notion “fair game” is martingale. In that context there is the classic “impossibility of gambling systems” result, with great conceptual and practical importance, but not mentioned here. Indeed the problems in this book are mostly “classic” in another sense, of referring to games of chance or to rather artificial “suppose” models chosen via some mathematical aesthetics, rather than realistic modeling of interesting chance phenomena outside the classroom. For the latter see

⭐, coincidently by another Biostatistician author.Disclaimer: The publishers sent me an unsolicited free copy.

⭐I think different people will have very different reactions to this book. Some will appreciate the selection of topics, the analysis, and the historical and biographical information. I personally have seen many other probability books, so that most, but not quite all, of this material was familiar. Fortunately, the author has made available a sample chapter through the Wiley web site, so the potential purchaser can make an informed decision.A review in the American Mathematical Society Notices suggested Mosteller’s Fifty Challenging Problems as containing similar material. Todhunter’s 19th century history of probability is freely available through archive.org and covers roughly half of this book’s topics.

⭐As a student, “Classic Problems of Probability” has complemented and enhanced my quantitative studies by offering a historical framework for many common theories and problems learned in statistics and probability.By relating not only the historical anecdotes but also the technical components of each “classic problem”, the author offers a complete text which allows the reader to appreciate the entirety of each problem without flipping between textbook and historical book (a unique attribute of this book).I would highly recommend this book to any person that is proficient in math(or interested in becoming so) as an excellent first venture into the history and technical explanation some very interesting classic problems of probability. Even if one is very well versed in this topic, there is likely something new to be learned in here- it covers so much ground and from a different point of view than most books.

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