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Probability Tales

Charles M. Grinstead, William P. Peterson, and J. Laurie Snell
Publisher: 
American Mathematical Society
Publication Date: 
2011
Number of Pages: 
237
Format: 
Paperback
Series: 
Student Mathematical Library 57
Price: 
42.00
ISBN: 
9780821852613
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
William J. Satzer
, on
08/29/2011
]

This book is the product of three authors who worked together on Chance News, an online newsletter that reviews current issues in the news relating to probability and statistics. Laurie Snell, in particular, was instrumental in getting Chance News started; he died last March. Although not designed as such, this book is a tribute to him and the project. Although the authors’ original intention was to select and expand a few of their favorite articles from Chance News, it turned out differently.

Indeed, it turned out to be a gem. Instead of many small chapters on a variety of topics, the book has four chapters, each of which explores a single topic in some depth. The emphasis is on applications of probability and statistics to everyday, real world events. Readers with basic knowledge of finite probability could get quite of bit from the book, but it is best suited for students with calculus and a bit more probability. This is a lively, conversational book, full of the good writing that has characterized Chance News over the years.

The first chapter investigates streaks, such as hot or cold streaks in sports, or good and bad runs in the stock market. Many sports fans believe in a version of the streak theory in basketball, for example, where a player who has made many consecutive baskets is said to have a “hot hand”. The authors take pains not to say that the streak theories are wrong; instead, they point out that many of the streaks observed in sports can be explained by a simple coin tossing model. The authors describe models for repeated trials (including Bernoulli and Markov chain models) and statistical tests on data from baseball, basketball, horseshoes, tennis and the stock market. (There is some evidence of streakiness in champion-level horseshoes and tennis.) The authors’ approach to this is nuanced — they recognize that human players are not coins, and that there are many complicating influences. One of the many strengths of the book is the authors’ ability to take a question and turn around and around to examine it from many sides without preconceived ideas. It’s a good model for students.

The remaining three chapters, each progressively shorter than the first, take up stock market returns, lotteries, and fingerprints. The discussion of the stock market has a nice treatment of the distribution of returns that compares and contrasts power law and normally distributed returns. With lotteries, the authors do standard stuff like computing odds of winning Powerball and finding the expected value of a lottery ticket, but they also have a number of great stories. (For example, the mystery of an unusually large number of winners of Powerball in 2005 was eventually attributed to a fortune cookie whose numbers several of the winners used.) The chapter on fingerprints is a narrative without much mathematics, but it addresses an important question in criminal law. How likely is it that a partial fingerprint (called a “latent”) is incorrectly matched to a properly prepared rolled fingerprint?

The book has an extensive bibliography and a modest number of exercises. This would be wonderful supplementary reading for a probability or statistics course. Any of its four chapters could also be the basis for an engaging independent study project.


Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.

  • Streaks
  • Modeling the stock market
  • Lotteries
  • Fingerprints
  • Answers to John Haigh's lottery questions
  • Bibliography
  • Index

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