This book, the second edition of a text that was first published around five years ago, is intended to make probability and statistics, along with some interesting applications, comprehensible to a general audience. It therefore competes with other books that have a similar purpose, such as Haigh’s Taking Chances (and a much shorter version of that book, Probability: A Very Short Introduction), Olofsson’s Probabilities: The Little Numbers that Rule Our Lives, Gould’s Mathematics in Games, Sports and Gambling, and Packel’s Mathematics of Games and Gambling.
Books like this, if they are mathematically sound and reasonably clearly written (as is Woolfson’s book), are, I think, quite valuable. There is a woeful ignorance of basic probability on the part of many people. This ignorance is reflected, to some extent, by the popularity of lottery games like Powerball, and at a more serious level it is reflected by the misuse of probabilistic reasoning in serious forums like courts of law. The famous People v. Collins case in California in the 1960s, or the Sally Clark homicide prosecution in England in the 1990s, both involved incorrect probabilistic reasoning (multiplication of probabilities of non-independent events); both of these cases are vividly discussed, for example, in the book Math on Trial: How Numbers Get Used and Abused in the Courtroom by Schneps and Colmez. Any book that can help alleviate some of this probabilistic illiteracy is, therefore, a good thing.
Books like this have an obvious value to mathematics instructors. Elementary discrete probability is an excellent topic, for example, for the kind of “quantitative literacy” courses that many colleges offer to non-majors to help fulfill a mathematics requirement: it is easy enough to be accessible to any reasonably hard-working student, and yet interesting enough to motivate many students.
In fact, for the last three years I have taught such a course at Iowa State University, the focus of which has been on applications of discrete probability to gambling; I have used at various times the books by Gould and Packel mentioned above, but am always on the lookout for any other book along similar lines.
The book under review might well be a good choice for such a course. It is, in terms of reader-friendliness, comparable to the books mentioned in the first paragraph, and strikes me as a book that should be successfully adapted as a text. One potential problem with doing so, however, is the exercises. There are not a lot of them, usually between 1 and 3 per chapter, and while they are sufficiently easy to assign in a liberal arts mathematics course, there are also solutions provided at the back of the book. Because of the easy access by students to solutions, and the relatively small number of problems, an instructor will almost certainly have to supplement them.
Woolfson’s book discusses both probability and statistics. The first few chapters develop the basic facts about probability and simple combinatorics and the rest of the book provides interesting applications. The choice of particular topics is for the most part fairly standard (the birthday problem is discussed, for example, and so are a number of common gambling games like roulette, craps, The UK National Lottery, and blackjack). On occasion, American readers may not immediately recognize a British term: I did not know until reading this book, for example, that the British card game Pontoon is our blackjack, and the game Crown and Anchor is essentially just the American carnival game Chuck-a-Luck (the latter term is not used). The book also covers what most of us refer to as the Monty Hall problem, but that phrase is, likewise, not used. (It seems a pity that the author didn’t talk about the wonderful controversy that arose with the Monty Hall problem and the famous column written by Marilyn vos Savant; my students find that story very interesting.)
In the area of statistics, we are given discussions of the Poisson and normal distributions (the author spends some time describing what the number e is; calculus is not used), as well as sections talking about sampling, variance and standard deviation.
Two chapters that are new to this edition discuss issues that appeared to me to be somewhat novel for a book at this level. There is a chapter entitled Science and Society that begins with a general look at the relationship between these two subjects (emphasizing that science can be counter-intuitive) and goes on to discuss in more detail subjects of contemporary interest such as meteorology, global warming and nuclear power generation. The discussion in this chapter seemed a bit more sophisticated than in previous chapters, but should be intelligible enough to give a general reader not only some idea of chaos theory but also some intelligent perspective on these problems.
The next chapter is on pensions, and, in particular, the problem of keeping pension systems solvent in view of increasing life expectancy. The discussion here is intentionally somewhat oversimplified and does not lead to any magic answers, only to the conclusion that there are no easy choices: to maintain a solvent system one needs to either increase contributions by the public, reduce the size of the payout or increase the age at which one is eligible for the pension. A student who reads this chapter, however, should be in a somewhat better position to understand discussions of Social Security, for example, that he or she is likely to read about in the newspaper.
Woolfson’s intent to make this book generally accessible does occasionally come at the expense of mathematical rigor. For example, he does not really give any definition for “independent events” but instead relies on the reader’s intuition that two events are independent if neither one affects the other; he then states as a fact that if events A and B are independent, then the probability that both A and B occur is the product of the probabilities of A and B — a fact which, of course, is generally taken as the definition of independence in more sophisticated books. As another example, technical terms are sometimes avoided altogether; I didn’t see the phrase “conditional probability” used in the text, but the concept does appear (as, for example, in the discussions of craps, both with fair and loaded dice). None of this bothered me at all; it seems an entirely reasonable way to make the ideas of the subject comprehensible to people without mathematical training. This is, after all, the objective of the text, and that objective has been met.
Mark Hunacek (firstname.lastname@example.org) teaches mathematics at Iowa State University.