Problems and snapshots from the world of probability. (English) Zbl 0785.60001

New York, NY: Springer-Verlag. xii, 240 p. (1994).
This fascinating and informative book contains 125 problems and snapshots from discrete probability theory. The problems are selected on the basis of their elegance and utility whereas snapshots are intended to provide a quick overview of topics in probability. The topics include classical combinatorics, classical random walk (Banach’s match box problem, etc.), problems of historical interest (Cardano, Huygens, Bernoulli, Petersburg paradox, Stirling numbers, Bayes), random permutations, coupon collecting, Poisson approximation, birthday problems, grouping by random division, records, ballot problems, urn models, cover times, card shuffling, Markov chains, patterns, embedding procedures, martingales, random walk on a chess board, rendevous problem. This book is written for a broad range of readers and serves as a lovely and important reminder even to researchers.
In the Preface, the authors write: “The first problem book of a similar kind as ours is perhaps F. Mosteller’s well-known ‘Fifty challenging problems in probability with solutions’ (1965, reprinted 1987; Zbl 0653.60001). Possibly, our book is the second.” Mosteller’s book might be the first but the present book is definitely not the second. Let me recall some related ones: G. L. Wise and E. B. Hall, Counterexamples in probability and real analysis (Oxford University Press, 1993); J. M. Stoyanov, Counterexamples in probability (1987; Zbl 0629.60001); and G. J. Székely, Paradoxes in probability theory and mathematical statistics (1986; Zbl 0605.60002). In spite of the existence of these and some other related books the present one is very valuable, very nice, and entertaining. The authors show an intimate knowledge over a wide range of stochastics and thus the readers can learn a lot.


60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60C05 Combinatorial probability