The ideas of probability are central to everyday life. Every day we are faced with the assessment of the risks of uncertain events. Decisions about whether we should take a life insurance policy, or if we should drive on the interstate in terrible weather, or if we should play the state lottery all involve understanding the outcome of a random event.
The study of random events is central to probability theory. However, most people have a poor understanding of the concept of randomness. For instance, it is often assumed that an event becomes more likely when it hasn't occurred.
Taking Chances: Winning with Probability is an introduction to probability theory that is intended for a general audience. It endeavors to explain probability while clarifying the concepts that often lead to common misconceptions. Often these misconceptions arise in games of chance. The book consists of short sections that aptly describe problems involving games of chance and uses only arithmetic and a small amount of algebra in its derivations. The author's intention is to overcome these common fallacies by clearly discussing and developing the relevant concepts. These intentions are well met in this text.
The writing style is very clear and polished. However, the style is somewhat formal at times. The book tends to read more like a textbook on probability rather than a book for the general audience. This is by no means a criticism, as the discussion and subsequent derivations are well written and can be easily followed. The mathematics level is higher than other popular texts on probability. D. Bennett's recent book Randomness is one such text that covers the essential elements of probability in a less mathematically demanding fashion.
Taking Chances tackles an impressive range of topics: lotteries, dice and card games, various casino games and racetrack betting. There is also a smattering of game theory, which includes a nice discussion of the Prisoner's Dilemma. While these topics are discussed, the basic laws of probability theory are motivated and used to solve the problem under consideration.
The discussion on betting schemes commonly used in the UK National lottery (as well as other lotteries), was interesting and enlightening. The schemes that people use for choosing their "winning" numbers range from picking important dates such as birthdays or holidays, to choosing the numbers based upon a particular pattern that the numbers form on the lottery ticket. The discussion is supported with actual weekly lottery data on the frequency of numbers selected, which I was unaware was publicly available.
As an aid for the reader to gauge their learning, the text includes "Test Yourself Quizzes." These quizzes cover ideas that have been discussed in the text as well as some extensions. The text includes detailed solutions to these quizzes in an appendix. This is a nice feature of the book that makes it convenient for self-study.
With the abundance of topics covered, as well as the problems included in the quiz sections, the text lends itself nicely as a supplement to courses in probability theory. As a supplement, the text might ideally work well in a junior level course in probability, where students often can benefit from studying the probabilities associated with realistic games of chance. In such a course, the quiz sections could be used as supplementary homework. The text could also be profitably used as a supplement for an introductory course in statistics or as a supplementary reading in a course in mathematics for the liberal arts student.
Having taught probability at various levels, I can say that a source, such as this text, with its wealth of information and examples, is a welcome addition.
D. J. Bennett. Randomness, Harvard University Press, 1998. ISBN 0674107454.
Randall J. Swift (firstname.lastname@example.org) is associate professor of mathematics at Western Kentucky University. His research interests include nonstationary stochastic processes, probability theory and mathematical modeling. He is a co-author of the MAA text A Course in Mathematical Modeling.
His non-mathematical interests are primarily devoted to his wife and three young daughters, but, when he has the time, he enjoys science fiction, history, listening to public radio, cooking and baseball.