Probabilities (eBook)

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.

Preface ix

Preface to the First Edition xi

1 Computing Probabilities: Right Ways and Wrong Ways 1

The Probabilist 1

The Probabilist's Toys and Language 4

The Probabilist's Rule Book 10

Independence, Airplanes, and Russian Peasants 15

Conditional Probability, Swedish TV, and British Courts 20

Liar, Liar 25

Car Dealers and Color Blindness 29

Shuttlecocks and Spaghetti Westerns 34

Combinatorics, Pastrami, and Poetry 40

The Von Trapps and The Binomial Distribution 45

Final Word 51

2 Surprising Probabilities: When Intuition Struggles 53

Boys, Girls, Aces, and Colored Cards 53

Goats and Gloats 58

Happy Birthday 61

Typical Atypicalities 66

The British Snob and I 72

Strategery 75

Final Word 78

3 Tiny Probabilities: Why Are They So Hard to Escape? 79

Probable Improbabilities 79

Saddam and I 83

Taking Tiny Risks 89

A Million-to-One Shot, Doc, Million to One! 91

Monsieur Poisson and the Mysterious Number 37 93

Clumps in Space 98

Final Word 100

4 Backward Probabilities: The Reverend Bayes to Our Rescue 101

Driving Miss Daisy 101

Bayes, Balls, and Boys (and Girls) 104

Bayes and My Green Card 107

Objection Your Honor 112

Ornithology 122

Final Word 125

5 Beyond Probabilities: What to Expect 127

Great Expectations 127

The Price is Right (Maybe) 134

Blood, Sweat, and Theory 137

Good Things Come to Those Who Wait 140

Expect the Unexpected 145

Exponential Growth toward Extinction 149

Size Matters (and Length, and Age) 159

Mean, Median, Mode 165

Deviant Behavior 171

Final Word 176

6 Inevitable Probabilities: Two Fascinating Mathematical Results 177

Alea Iacta Est, Over and Over 177

Even-Steven? The Law Misunderstood 181

Coin Tosses and Freeway Congestion 188

Let's Get Serious 195

Bells and Bread 200

How a Toronto Quincunx Changed My Life 204

Final Word 206

7 Gambling Probabilities: Why Donald Trump Is Richer than You 209

French Letters 209

Roulette: A Classy Way to Waste Your Money 214

Craps: Not so Dicey after All 219

Blackjack: Money for Mnemonics 222

Math for Losers 227

Win Money and Lose Friends 234

Final Word 245

8 Guessing Probabilities: Enter the Statisticians 247

Lies, Damned Lies, and Beautiful Lies? 247

4 Out of 10 Like the President 19 Times Out of 20 251

Polls Gone Wild 257

The Silver Lining 262

The Lawsuit and the Lurker 265

Football Players and Geyser Eruptions 271

Snooping in the Abbot's Garden 278

Final Word 284

9 Faking Probabilities: Computer Simulation 285

Mahogany Dice and Modular Arithmetic 285

Random and Not-So-Random Digits 293

Number One is Number One 294

Is Random Really Random? 297

Final Word 302

Index 305

"The book 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." (Zentralblatt MATH, 1 June 2015)