Digital Dice: Computational Solutions to Practical Probability Problems
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"Paul Nahin's Digital Dice is a marvelous book, one that is even better than his Duelling Idiots. Nahin presents twenty-one great probability problems, from George Gamow's famous elevator paradox (as corrected by Donald Knuth) to a bewildering puzzle involving two rolls of toilet paper, and he solves them all with the aid of Monte Carlo simulations and brilliant, impeccable reasoning."--Martin Gardner"Nahin's new book is a rich source of tantalizing, real-life probability puzzles that require considerable ingenuity, and in most cases computer simulation, to solve. Though written to be delved into rather than read cover-to-cover, Digital Dice has an engaging and often witty style that makes each chapter a pleasurable read."--Keith Devlin, author of The Math Gene and The Math Instinct"Open this delightful, matchless book to be sucked into a treasure trove of wonderful conundrums of everyday life. Then, persuaded by straightforward Monte Carlo simulation exercises, emerge refreshed, invigorated, and fully satisfied by the unique experience of learning from Nahin's marvelous Digital Dice."--Joseph Mazur, author of The Motion Paradox"One of the strengths of Digital Dice is its wealth of historical information. Nahin carefully notes the origin of each problem and traces its history. He also tells a number of amusing anecdotes. I found all the problems interesting, especially Parrondo's Paradox. Anyone who has not met this paradox will be amazed by it! Digital Dice is a very enjoyable read."--Nick Hobson, creator of the award-winning Web site Nick's Mathematical Puzzles"By presenting problems for which complete theoretical analysis is difficult or currently impossible, Digital Dice is a reminder that mathematics is often advanced by investigation, long before theoretical tools are brought to bear. The book's choice of problems is eclectic and interesting, and the explanations are clear and easy to read. A welcome addition to popular mathematical literature."--Julian Havil, author of Nonplussed!: Mathematical Proof of Implausible Ideas James M. Cargal - The UMAP Journal All of the books by Nahin and Havil are worth having, including others not listed here. I particularly recommend Digital Dice for the task of teaching undergraduates in mathematics the fundamentals of computation and simulation.
Introduction 1The Problems 35The Clumsy Dishwasher Problem 37Will Lil and Bill Meet at the Malt Shop? 38A Parallel Parking Question 40A Curious Coin-Flipping Game 42The Gamow-Stern Elevator Puzzle 45Steve's Elevator Problem 48The Pipe Smoker's Discovery 51A Toilet Paper Dilemma 53The Forgetful Burglar Problem 59The Umbrella Quandary 61The Case of the Missing Senators 63How Many Runners in a Marathon? 65A Police Patrol Problem 69Parrondo's Paradox 74How Long Is the Wait to Get the Potato Salad? 77The Appeals Court Paradox 81Waiting for Buses 83Waiting for Stoplights 85Electing Emperors and Popes 87An Optimal Stopping Problem 91Chain Reactions, Branching Processes, and Baby Boys 96MATLAB Solutions To The Problems 101The Clumsy Dishwasher Problem 103Will Lil and Bill Meet at the Malt Shop? 105A Parallel Parking Question 109A Curious Coin-Flipping Game 114The Gamow-Stern Elevator Puzzle 120Steve's Elevator Problem 124The Pipe Smoker's Discovery 129A Toilet Paper Dilemma 140The Forgetful Burglar Problem 144The Umbrella Quandary 148The Case of the Missing Senators 153How Many Runners in a Marathon? 157A Police Patrol Problem 160Parrondo's Paradox 169How Long is the Wait to Get the Potato Salad? 176The Appeals Court Paradox 184Waiting for Buses 187Waiting for Stoplights 191Electing Emperors and Popes 197An Optimal Stopping Problem 204Chain Reactions, Branching Processes, and Baby Boys 213One Way to Guess on a Test 221An Example of Variance-Reduction in the Monte Carlo Method 223Random Harmonic Sums 229Solving Montmort's Problem by Recursion 231An Illustration of the Inclusion-Exclusion Principle 237Solutions to the Spin Game 244How to Simulate Kelvin's Fair Coin with a Biased Coin 248How to Simulate an Exponential Random Variable 252Index to Author-Created MATLAB m-Files in the Book 255Glossary 257Acknowledgments 259Index 261
