Duelling Idiots and Other Probability Puzzlers
What are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of 212 puzzles, the author challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper; and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the working of probability. Over the years, the author, a veteran writer and teacher of the subject, has collected these and other favourite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? what are the chance it will snow on your birthday in any given year? how can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions?
The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly", for example, is a clever variation of a "random walk" problem,, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical materials, this book should be of interest for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.
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What Reviewers Are Saying
"By following Nahin's informal style it is possible to set [the examples] up quickly from first principles and slip them into courses on calculus, algebra, or scientific programming. They also offer a wealth of topics for undergraduate projects. Those duelling idiots are fighting over a goldmine."--Des Higham, "MSOR Connections"
It is said that Stephen Hawking, author of the book A Brief History of Time, was told that sales would be proportionately less for every mathematical equation he included. He included just one nevertheless and the rest, as they say, is history. Here on the other hand is a bok of which it is almost true to say that it is mostly equations. It starts with the words 'This is a book for those who really like probability problems'. And it has a habit of dropping in phrases saying that a particular problem 'uses only the most elementary of arithmetic methods' or 'can be solved by simple counting', before dropping into another round of what, for many, will be exotic calculations and equations. That said this is an eye-opener in the way it highlights the counter-intuitive aspects of probability theory. It is largely in the form of sections setting out problems and then, in the latter part of the book, showing how the solution can be arrived at (and how this can link to computer programmes). A few questions - what are the chances that it will snow on your birthday? - are perhaps not in themselves useful. They are literally examples to demonstrate the methodology. Some examples, however, pose potentially useful questions: how many children are you likely to have before you have representatives of each sex? (a problem described as 'not very hard to do mathematically'). The author, Professor of Electrical Engineering at the University of New Hampshire, has written widely on such topics. For those who are both interested and able to follow the maths, this is likely to be a fascinating read. It is not, however, the place to make a first foray into examining probability theory - it will probably put the newcomer off for life. (Kirkus UK)