Digital Dice: Computational Solutions to Practical Probability Problems (New in Paperback) (Princeton Puzzlers)
Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations.
Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women.
The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem.
Digital Dice will appeal to anyone who enjoys popular math or computer science. In a new preface, Nahin wittily addresses some of the responses he received to the first edition.
Table of Contents
The Problems 35
1. The Clumsy Dishwasher Problem 37
2. Will Lil and Bill Meet at the Malt Shop? 38
3. A Parallel Parking Question 40
4. A Curious Coin-Flipping Game 42
5. The Gamow-Stern Elevator Puzzle 45
6. Steve’s Elevator Problem 48
7. The Pipe Smoker’s Discovery 51
8. A Toilet Paper Dilemma 53
9. The Forgetful Burglar Problem 59
10. The Umbrella Quandary 61
11. The Case of the Missing Senators 63
12. How Many Runners in a Marathon? 65
13. A Police Patrol Problem 69
14. Parrondo’s Paradox 74
15. How Long Is the Wait to Get the Potato Salad? 77
16. The Appeals Court Paradox 81
17. Waiting for Buses 83
18. Waiting for Stoplights 85
19. Electing Emperors and Popes 87
20. An Optimal Stopping Problem 91
21. Chain Reactions, Branching Processes, and Baby Boys 96
MATLAB Solutions To The Problems 101