Duelling Idiots and Other Probability Puzzlers

Duelling Idiots and Other Probability Puzzlers

Paul J. Nahin
Copyright Date: 2000
Pages: 280
https://www.jstor.org/stable/j.ctt7ssjr
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  • Book Info
    Duelling Idiots and Other Probability Puzzlers
    Book Description:

    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 twenty-one puzzles, Paul Nahin 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 workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite 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 chances 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 material,Duelling Idiotsis ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.

    eISBN: 978-1-4008-4304-6
    Subjects: Mathematics, Statistics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. Table of Contents
    (pp. vii-viii)
  3. Acknowledgments
    (pp. ix-x)
  4. Preface to the Paperback Edition
    (pp. xi-xx)
  5. Preface
    (pp. xxi-2)
  6. Introduction
    (pp. 3-14)

    This is a book for people who really like probability problems. There are, I think, a lot of people who fall into that category. Indeed, the editors ofParade, a magazine insert in millions of Sunday newspapers across America, thought a probabilistic question intriguing enough to put it on the cover of their issue of August 10, 1997. For the real connoisseur of probability, however, it was actually a pretty tame problem: "Your dog has a litter of four. Is it most likely that two are males and two are females?"

    That question was posed in the "Ask Marilyn" column...

  7. The Problems
    (pp. 15-80)

    Suppose you are assigned the following task: You are to determine the fraction of the population that practices a certain private act (use your imagination). If you could gather a large number of randomly selected people together into a large room or auditorium, you could then simply have each person fill out an anonymous questionnaire. Since no one could be identified from such a form, people would presumably tell the truth. But suppose this is not possible, and your task is to be accomplished over time through individual encounters. It is clear that you cannot just ask people, because they...

  8. The Solutions
    (pp. 81-174)

    Suppose there arempeople in your survey and that we let Y denote the total number of YES answers. With probability$\frac{1}{2}$, the coin shows tails on the first flip, so$\frac{1}{2}m$people will answer the EQ. (This argument is implicitly assuming thatmis large.) For the other$\frac{1}{2}m$people, who flip the coin a second time, half will answer YES (the second flip showed heads) and half will answer NO (the second flip did not show heads). That is,$\frac{1}{4}m$YES answers are for the non-EQ. So,$Y - \frac{1}{4}m$YES answers are for the EQ, generated from...

  9. Random Number Generators
    (pp. 175-197)

    The very idea of a deterministic machine like a computer creating random numbers seems to be an oxymoron. Random numbers are, well,random, while a computer is supposed to be an utterly predictable gadget. Indeed, no one has ever seen an advertisement saying something like

    BUY OUR NEW SUPER MEGABLASTER COMPUTER!

    YOU NEVER KNOW WHAT IT WILL DO!

    DON’T BUY A DULL, BORING, PREDICTABLE COMPUTER;

    BUY OURS AND BE SURPRISED EVERY TIME YOU TURN IT ON!

    Would you buy such a machine? Probably not. And in fact, modern computers actually generate what are more precisely calledpseudo-random numbers; that is,...

  10. “Some Things Just Have to Be Done by Hand!”
    (pp. 198-201)

    The Most Important Entity rubbed His temples in fatigue. There was just so damned much crap to put up with nowadays. The personnel paperwork was nearly overwhelming, even for a being with omnipotent powers. And a work force faced with zero turnover had a first-class morale problem. The younger ones knew there was no hope for advancement by the once-usual routes of death, retirement, or resignation. None of those events ever happened—here.

    The telephone rang, and He answered in weary relief at the distraction. “Yes?”

    “Sorry to bother you, Sir, but the main computers have a backlog in the...

  11. MATLAB Programs
    (pp. 202-266)
  12. Index
    (pp. 267-270)
  13. Back Matter
    (pp. 271-271)