This nice little book by Grinstead, Peterson and Snell is devoted to four real world applications of probability theory. While the technical level is kept at a minimum, the authors focus on explaining how the real world problems can be translated into the language of probability and spend large parts of the text on motivating the models they use. This is mostly done by a large number of plots such that also readers with less mathematical background get a good feeling for the intuition behind the models.
The first problem deals with the idea of streaks. The motivation is taken from sports like basketball or baseball, and the author discusses the question if streaky behavior can be reasonably modeled by a simple coin-tossing model. Therefore, the authors introduce the Bernoulli model, where the probability of success for each trial is a constant, and apply simple statistical tests to assess whether the success probability is different from one half for data from various sports.
The second application takes the reader to the stock market. Here, the main question of interest is which distributions give good models for return distributions.
The third chapter is on power ball lottery. The authors explain in detail how the probabilities of winning can be calculated, what the expected winning is, and they also speak about lottery systems.
The last real world problem asks how likely it is that two fingerprints coincide when a more or less accurate image of them is given. This question is of course highly relevant for our legal system and I was very surprised to learn that in the US no standard test for fingerprint comparison is defined.
It was a great pleasure for me to read this book. In many parts, it reads almost like a novel but of course a very instructive one. At the same time, the text is a valuable source for any course on basic probability in giving a very detailed picture of how the theory can be used in real world applications.