Probabilities: The Little Numbers That Rule Our Lives

Praise for the First Edition “If there is anything you want to know, or remind yourself, about probabilities, then look no further than this comprehensive, yet wittily written and enjoyable, compendium of how to apply probability calculations in real–world situations.” – Keith Devlin, Stanford University, National Public Radio’s “Math Guy” and author of The Math Gene and The Unfinished Game From probable improbabilities to regular irregularities, Probabilities: The Little Numbers That Rule Our Lives, Second Edition investigates the often surprising effects of risk and chance in our lives. Featuring a timely update, the Second Edition continues to be the go–to guidebook for an entertaining presentation on the mathematics of chance and uncertainty. The new edition develops the fundamental mathematics of probability in a unique, clear, and informal way so readers with various levels of experience with probability can understand the little numbers found in everyday life. Illustrating the concepts of probability through relevant and engaging real–world applications, the Second Edition features numerous examples on weather forecasts, DNA evidence, games and gambling, and medical testing. The revised edition also includes: Applications of probability in finance, such as option pricing The introduction of branching processes and the extinction of family names An extended discussion on opinion polls and Nate Silver’s election predictions Probabilities: The Little Numbers That Rule Our Lives, Second Edition is an ideal reference for anyone who would like to obtain a better understanding of the mathematics of chance, as well as a useful supplementary textbook for students in any course dealing with probability. Peter Olofsson, PhD, is Professor in the Department of Mathematics at Trinity University, USA. An active researcher in the field of applied probability and an experienced teacher, Dr. Olofsson is the author of Probability, Statistics, and Stochastic Processes, Second Edition , also published by Wiley.  

Contents Preface v 1 Computing Probabilities: Right Ways and Wrong Ways 1 The Probabilist 1 The Probabilist’s Toys and Language 4 The Probabilist’s Rule Book 9 Independence, Airplanes, and Russian Peasants 14 Conditional Probability, Swedish TV, and British Courts 19 Liar, Liar 25 Car Dealers and Color Blindness 28 Shuttlecocks and Spaghetti Westerns 33 Combinatorics, Pastrami, and Poetry 39 The von Trapps and the Binomial Distribution 44 Final Word 49 2 Surprising Probabilities: When Intuition Struggles 51 Boys, Girls, Aces, and Colored Cards 51 Goats and Gloats 56 Happy Birthday 58 Typical Atypicalities 63 The British Snob and I 69 Strategery 72 Final Word 75 3 Tiny Probabilities: Why Are They So Hard to Escape? 77 Probable Improbabilities 77 Saddam and I 81 Taking Tiny Risks 86 A Million–to–One Shot, Doc, Million to One! 88 Monsieur Poisson and the Mysterious Number 37 90 Clumps in Space 95 Final Word 97 4 Backward Probabilities: The Reverend Bayes to Our Rescue 99 Driving Miss Daisy 99 Bayes, Balls, and Boys (and Girls) 102 Bayes and My Green Card 105 Objection Your Honor 110 Ornithology 119 Final Word 122 5 Beyond Probabilities: What to Expect 125 Great Expectations 125 The Price is Right (Maybe) 131 Blood, Sweat, and Theory 135 Good Things Come to Those Who Wait 137 Expect the Unexpected 142 Exponential growth toward extinction 146 Size Matters (and Length, and Age) 156 Mean, median, mode 161 Deviant Behavior 167 Final Word 172 6 Inevitable Probabilities: Two Fascinating Mathematical Results 173 Alea Iacta Est, Over and Over 173 Even–Steven? The Law Misunderstood 177 Coin Tosses and Freeway Congestion 183 Let’s Get Serious 190 Bells and Bread 194 How a Toronto Quincunx Changed My Life 199 Final Word 201 7 Gambling Probabilities: Why Donald Trump Is Richer than You 203 French Letters 203 Roulette: A Classy Way to Waste Your Money 207 Craps: Not so Dicey After All 212 Blackjack: Money for Mnemonics 215 Math for Losers 221 Win Money and Lose Friends 228 Final Word 238 8 Guessing Probabilities: Enter the Statisticians 239 Lies, Damned Lies, and Beautiful Lies? 239 4 out of 10 Like the President 19 Times out of 20 243 Polls Gone Wild 248 The Silver Lining 253 The Lawsuit and the Lurker 257 Football Players and Geyser Eruptions 262 Snooping in the Abbot’s Garden 269 Final Word 274 9 Faking Probabilities: Computer Simulation 277 Mahogany Dice and Modular Arithmetic 277 Random and Not–So–Random Digits 284 Number One Is Number One 285 Is Random Really Random? 288 Final Word 293 Index 295

Peter Olofsson, PhD, is Professor in the Department of Mathematics at Trinity University, USA. An active researcher in the field of applied probability and an experienced teacher, Dr. Olofsson is the author of Probability, Statistics, and Stochastic Processes, Second Edition , also published by Wiley.