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Summary Table of Contents Author Biography

Detailing the history of probability, this book examines the classic problems of probability that have shaped the field and emphasizes problems that are counter-intuitive by nature. Classic Problems of Probability is rich in the hostory of probability while keeping the explanations and discussions as accessible as possible. Each of 35 presented problems end with a listing of the latest relevant publications on the topic, and the author provides detailed and rigorous mathematical proofs as needed. For example, in the discussion of the Buffon nee... MOREdle problem, readers will find much more than the conventional discussion found in other books on the topic. The author discusses alternative proofs by Barbier that lead to much more profound and general results. The choice of random variables for which a uniform distribution is possible is also presented, which then naturally leads to a discussion on invariance. Likewise, the discussion of Bertrand's chord paradox involves much more than stating there are three well-known possible solutions to the problems; rather, the athor discusses the implications of the indeterminacy of the problem as well as the contributions made by Poincare and Jaynes. This approach was used for all of the problems in the book.

"A great book, one that I will certainly add to my personal library." - Paul J. Nahin, Professor Emeritus of Electrical Engineering, University of New Hampshire Classic 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 invariance Various paradoxes raised by Joseph Bertrand Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem The Bayesian paradigm and various philosophies of probability Coverage of both elementary and more complex problems, including the Chevalier de M�r� problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox Classic 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.

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 Hampshire

Classic 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 invariance
Various paradoxes raised by Joseph Bertrand
Classic problems in decision theory, including Pascal's Wager, Kraitchik's Neckties, and Newcomb's problem
The Bayesian paradigm and various philosophies of probability
Coverage of both elementary and more complex problems, including the Chevalier de M�r� problems, Fisher and the lady testing tea, the birthday problem and its various extensions, and the Borel-Kolmogorov paradox

Classic 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.

... MORE

Preface	p. ix
Acknowledgments	p. xi
Cardano and Games of Chance (1564)	p. 1
Galileo and a Discovery Concerning Dice (1620)	p. 9
The Chevalier de M�r� Problem I: The Problem of Dice (1654)	p. 13
The Chevalier de M�r� Problem H: The Problem of Points (1654)	p. 20
Huygens and the Gambler's Ruin (1657)	p. 39
The Pepys-Newton Connection (1693)	p. 49
Rencontres with Montmort (1708)	p. 54
Jacob Bernoulli and his Golden Theorem (1713)	p. 62
De Moivre's Problem (1730)	p. 81
De Moivre, Gauss, and the Normal Curve (1730, 1809)	p. 89
Daniel Bernoulli and the St Petersburg Problem (1738)	p. 108
d'Alembert and the "Croix ou Pile" Article (1754)	p. 119
d'Alembert and the Gambler's Fallacy (1761)	p. 124
Bayes, Laplace, and Philosophies of Probability (1764, 1774)	p. 129
Leibniz's Error (1768)	p. 156
The Buffon Needle Problem (1777)	p. 159
Bertrand's Ballot Problem (1887)	p. 169
Bertrand's Strange Three Boxes (1889)	p. 175
Bertrand's Chords (1889)	p. 179
Three Coins and a Puzzle from Galton (1894)	p. 186
Lewis Carroll's Pillow Problem No. 72 (1894)	p. 189
Borel and a Different Kind of Normality (1909)	p. 194
Borel's Paradox and Kolmogorov's Axioms (1909, 1933)	p. 199
Of Borel, Monkeys, and the New Creationism (1913)	p. 208
Kraitchik's Neckties and Newcomb's Problem (1930, 1960)	p. 215
Fisher and the Lady Tasting Tea (1935)	p. 224
Benford and the Peculiar Behavior of the First Significant Digit (1938)	p. 233
Coinciding Birthdays (1939)	p. 240
L�vy and the Arc Sine Law (1939)	p. 247
Simpson's Paradox (1951)	p. 253
Gamow, Stern, and Elevators (1958)	p. 260
Monty-Hall, Cars, and Goats (1975)	p. 264
Parrondo's Perplexing Paradox (1996)	p. 271
Bibliography	p. 277
Photo Credits	p. 296
Index	p. 299
Table of Contents provided by Ingram. All Rights Reserved.

Prakash Gorroochurn, PhD, is Assistant Professor in the Department of Biostatistics at Columbia University, where he is also a statistical consultant in the School of Social Work. Dr. Gorroochurn has published extensively in his areas of research interest, which include mathematical population genetics and genetic epidemiology.

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