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Classic Problems of Probability

Book Description

"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 Méré 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.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Dedication
  5. Preface
  6. Acknowledgments
  7. Problem 1: Cardano and Games of Chance (1564)
    1. 1.1 Discussion
  8. Problem 2: Galileo and A Discovery Concerning Dice (1620)
    1. 2.1 Discussion
  9. Problem 3: The Chevalier de Méré Problem I: The Problem of Dice (1654)
    1. 3.1 Discussion
  10. Problem 4: The Chevalier de Méré Problem II: The Problem of Points (1654)
    1. 4.1 Discussion
  11. Problem 5: Huygens and the Gambler's Ruin (1657)
    1. 5.1 Discussion
  12. Problem 6: The Pepys–Newton Connection (1693)
    1. 6.1 Discussion
  13. Problem 7: Rencontres with Montmort (1708)
    1. 7.1 Discussion
  14. Problem 8: Jacob Bernoulli and His Golden Theorem (1713)
    1. 8.1 Discussion
  15. Problem 9: De Moivre's Problem (1730)
    1. 9.1 Discussion
  16. Problem 10: De Moivre, Gauss, and the Normal Curve (1730, 1809)
    1. 10.1 Discussion
  17. Problem 11: Daniel Bernoulli and the St: Petersburg Problem (1738)
    1. 11.1 Discussion
  18. Problem 12: D'Alembert and the “Croix ou Pile” Article (1754)
    1. 12.1 Discussion
  19. Problem 13: D'Alembert and the Gambler's Fallacy (1761)
    1. 13.1 Discussion
  20. Problem 14: Bayes, Laplace, and Philosophies of Probability (1764, 1774)
    1. 14.1 Discussion
  21. Problem 15: Leibniz's Error (1768)
    1. 15.1 Discussion
  22. Problem 16: The Buffon Needle Problem (1777)
    1. 16.1 Discussion
  23. Problem 17: Bertrand's Ballot Problem (1887)
    1. 17.1 Discussion
  24. Problem 18: Bertrand's Strange Three Boxes (1889)
    1. 18.1 Discussion
  25. Problem 19: Bertrand's Chords (1889)
    1. 19.1 Discussion
  26. Problem 20: Three Coins and A Puzzle from Galton (1894)
    1. 20.1 Discussion
  27. Problem 21: Lewis Carroll's Pillow Problem No: 72 (1894)
    1. 21.1 Discussion
  28. Problem 22: Borel and A Different Kind of Normality (1909)
    1. 22.1 Discussion
  29. Problem 23: Borel's Paradox and Kolmogorov's Axioms (1909, 1933)
    1. 23.1 Discussion
  30. Problem 24: Of Borel, Monkeys, and the New Creationism (1913)
    1. 24.1 Discussion
  31. Problem 25: Kraitchik's Neckties and Newcomb's Problem (1930, 1960)
    1. 25.1 Discussion
  32. Problem 26: Fisher and the Lady Tasting Tea (1935)
    1. 26.1 Discussion
  33. Problem 27: Benford and the Peculiar Behavior of the First Significant Digit (1938)
    1. 27.1 Discussion
  34. Problem 28: Coinciding Birthdays (1939)
    1. 28.1 Discussion
  35. Problem 29: Lévy and the Arc Sine Law (1939)
    1. 29.1 Discussion
  36. Problem 30: Simpson's Paradox (1951)
    1. 30.1 Discussion
  37. Problem 31: Gamow, Stern, and Elevators (1958)
    1. 31.1 Discussion
  38. Problem 32: Monty Hall, Cars, and Goats (1975)
    1. 32.1 Discussion
  39. Problem 33: Parrondo's Perplexing Paradox (1996)
    1. 33.1 Discussion
  40. Bibliography
  41. Photo Credits
  42. Index