# Duelling Idiots and Other Probability Puzzlers

Paul J. Nahin
Pages: 280
https://www.jstor.org/stable/j.ctt7ssjr

1. Front Matter
(pp. i-vi)
(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)