Digital Dice: Computational Solutions to Practical Probability Problems

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.

Table of Contents

1. The Clumsy Dishwasher Problem
2. Will Lil and Bill Meet at the Malt Shop?
3. A Parallel Parking Question
4. A Curious Coin-Flipping Game
5. The Gamow-Stern Elevator Puzzle
6. Steve’s Elevator Problem
7. The Pipe Smoker’s Discovery
8. A Toilet Paper Dilemma
9. The Forgetful Burglar Problem
10. The Umbrella Quandary
11. The Case of the Missing Senators
12. How Many Runners in a Marathon?
13. A Police Patrol Problem
14. Parrondo’s Paradox
15. How Long Is the Wait to Get the Potato Salad?
16. The Appeals Court Paradox
17. Waiting for Buses
18. Waiting for Stoplights
19. Electing Emperors and Popes
20. An Optimal Stopping Problem
21. Chain Reactions, Branching Processes, and Baby Boys