Will You Be Alive 10 Years from Now?: And Numerous Other Curious Questions in Probability

by Paul Nahin

Overview

A collection of stimulating probability puzzles from bestselling math writer Paul Nahin

What are the chances of a game-show contestant finding a chicken in a box? Is the Hanukkah dreidel a fair game? Will you be alive ten years from now? These are some of the one-of-a-kind probability puzzles that popular math writer Paul Nahin offers in this lively and informative book. Nahin brings probability to life with colorful historical anecdotes and a unique puzzle-solving approach that illustrates many of the techniques mathematicians use to grapple with probability. He looks at classic puzzles—from Galileo's dice-tossing problem to a disarming dice puzzle that would have astonished even Newton—and presents a dozen challenge problems and twenty-five probability puzzlers. With wit and insight, Nahin demonstrates why seemingly simple probability problems can stump even the experts.

Product Details

ISBN-13:	9780691196367
Publisher:	Princeton University Press
Publication date:	11/12/2019
Edition description:	Reprint
Pages:	256
Product dimensions:	5.60(w) x 8.80(h) x 0.80(d)

About the Author

Paul J. Nahin is the author of many popular math books, including How to Fall Slower Than Gravity, In Praise of Simple Physics, and An Imaginary Tale (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

Table of Contents

Preface xv
Introduction: Classic Puzzles from the Past 1
I.1 A Gambling Puzzle of Gombaud and Pascal 1
I.2 Galileo's Dice Problem 3
I.3 Another Gombaud-Pascal Puzzle 4
I.4 Gambler's Ruin and De Moivre 6
I.5 Monte Carlo Simulation of Gambler's Ruin 10
I.6 Newton's Probability Problem 13
I.7 A Dice Problem That Would Have Surprised Newton 17
I.8 A Coin-Flipping Problem 18
I.9 Simpson's Paradox, Radio-Direction Finding, and the Spaghetti Problem 21
Challenge Problems 30
1Breaking Sticks 36
1.1 The Problem 36
1.2 Theoretical Analysis 36
1.3 Computer Simulation 38
2The Twins 42
2.1 The Problem 42
2.2 Theoretical Analysis 43
2.3 Computer Simulation 44
3Steve's Elevator Problem 47
3.1 The Problem 47
3.2 Theoretical Analysis by Shane Henderson 48
3.3 Computer Simulation 51
4Three Gambling Problems Newton Would "Probably" Have Liked 52
4.1 The Problems 52
4.2 Theoretical Analysis 1 54
4.3 Computer Simulation 1 55
4.4 Theoretical Analysis 2 57
4.5 Computer Simulation 2 58
4.6 Theoretical Analysis 3 59
5Big Quotients—Part 1 62
5.1 The Problem 62
5.2 Theoretical Analysis 62
5.3 Computer Simulation 64
6Two Ways to Proofread 66
6.1 The Problem 66
6.2 Theoretical Analysis 67
7Chain Letters That Never End 70
7.1 The Problem 70
7.2 Theoretical Analysis 70
8Bingo Befuddlement 74
8.1 The Problem 74
8.2 Computer Simulation 75
9Is Dreidel Fair? 79
9.1 The Problem 79
9.2 Computer Simulation 80
10Hollywood Thrills 83
10.1 The Problem 83
10.2 Theoretical Analysis 83
11The Problem of the n-Liars 87
11.1 The Problem 87
11.2 Theoretical Analysis 87
11.3 Computer Simulation 89
12The Inconvenience of a Law 90
12.1 The Problem 90
12.2 Theoretical Analysis 90
13A Puzzle for When the Super Bowl is a Blowout 93
13.1 The Problem 93
13.2 Theoretical Analysis 94
14Darts and Ballistic Missiles 96
14.1 The Problem 96
14.2 Theoretical Analysis 97
15Blood Testing 103
15.1 The Problem 103
15.2 Theoretical Analysis 103
16Big Quotients—Part 2 107
16.1 The Problem 107
16.2 Theoretical Analysis 107
17To Test or Not to Test? 117
17.1 The Problem 117
17.2 Theoretical Analysis 119
18Average Distances on a Square 126
18.1 The Problem(s) 126
18.2 Theoretical Analyses 127
18.3 Computer Simulations 136
19When Will the Last One Fail? 139
19.1 The Problem 139
19.2 Theoretical Analyses 142
20Who's Ahead? 147
20.1 The Problem 147
20.2 Theoretical Analysis 148
21Plum Pudding 151
21.1 The Problem 151
21.2 Computer Simulation 152
21.3 Theoretical Analysis 153
22Ping-Pong, Squash, and Difference Equations 156
22.1 Ping-Pong Math 156
22.2 Squash Math Is Harder! 161
23Will You Be Alive 10 Years from Now? 168
23.1 The Problem 168
23.2 Theoretical Analysis 169
24Chickens in Boxes 176
24.1 The Problem (and Some Warm-ups, Too) 176
24.2 Theoretical Analysis 180
25Newcomb's Paradox 183
25.1 Some History 183
25.2 Decision Principles in Conflict 186
Challenge Problem Solutions 189
Technical Note on MATLAB®'s Random Number Generator 213
Acknowledgments 217
Index 219

What People are Saying About This

From the Publisher

"Readers of this absorbing book will gain significant pleasure as well as a broadened understanding of the nuances of mathematics, along with a wonderful picture of how analytics and simulations complement each other. Nahin is a master at this. I love this book!"—Joseph Mazur, author of What's Luck Got to Do with It?: The History, Mathematics, and Psychology of the Gambler's Illusion

"This book will be of interest to anyone who loves the challenge and surprise inherent in probability theory, and who likes to tinker with their computer as a simulator. Nahin's style is easy and informal."—Julian Havil, author of The Irrationals: A Story of the Numbers You Can't Count On

Editorial Reviews

10/07/2013
Nahin (Duelling Idiots and Other Probability Puzzlers), University of New Hampshire professor emeritus of electrical engineering, takes intrepid, mathematically minded readers on a fresh outing through the land of probability in this collection of puzzles, complete with MATLAB computer code. Nahin draws from the usual venues of probability problems, from gambling to sports, many utilizing Monte Carlo algorithms, which use random numbers to describe the behavior of dice and flipped coins. Nahin begins with the familiar “Gambler’s Ruin” problem, then branches out to consider the number of stops an elevator might make along its route, the likelihood of a proofreader missing errors, chance of false positives in medical tests, and whether the traditional dreidel game is really fair. The book isn’t written for the casual browser; Nahin assumes readers will have a solid grounding in college-level mathematics as well as basic probability and some computer programming, if not knowledge of the MATLAB software package. For those who have the prerequisites, the author offers a pleasant collection of brain-teasers on which to test their mettle. 28 line illus., 22 tables. (Dec.)

Publishers Weekly

"Prolific mathematics author Nahin presents a series of thought-provoking probability questions designed to intrigue the reader. . . . In general, the solutions rely only on basic rules of probability and algebraic manipulation, while ranging in difficulty from the very straightforward to the highly challenging."

Choice

"A wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle."—-Harold D. Shane, Library Journal

From the Publisher

"For mathematicians with an interest in probability theory, this is a fun holiday book."

Eos blog

09/15/2013
Problems involving counting and probability can be challenging to even the best mathematicians. Nahin (electrical engineering, emeritus, Univ. of New Hampshire; Chases and Escapes) begins by summarizing some of the better-known historical puzzles. He then moves on to 25 lesser-known but equally compelling examples—one per chapter—in an entertaining and yet relatively rigorous style. In addition, he includes a dozen challenge problems for the reader (the solutions are provided in the back of the book). Probability questions frequently give rise to counterintuitive answers; many here fall into that category. Even supplied with the correct theoretical solutions, many of us have trouble believing them. The author names computer programs that can be used to do Monte Carlo simulations of his examples to convince us further of their correctness. VERDICT Fair warning: competence in a university-level, post-calculus course in probability is a prerequisite to understanding much of this material. Some experience with Markov Chains, difference equations, and computer literacy is also helpful. This is a wonderful book for trained math lovers who enjoy the mental stimulation provided by a good mathematics puzzle.—Harold D. Shane, Emeritus, Baruch Coll., CUNY

Library Journal