The Probability Lifesaver: All the Tools You Need to Understand Chance

Steven J. Miller’s The Probability Lifesaver presents, as its subtitle claims, “all the tools you need to understand chance” in a clear, straightforward manner. In the introduction to the reader, Miller describes that the book is designed to either be a standard textbook for a probability course or as a supplement to a standard textbook; and it does not disappoint. From my experience teaching probability this book would serve well as a supplement, but others may choose to use it as a primary source.

Throughout the hefty book (727 pages) many examples are provided that can be used, perused or even skipped altogether at one’s discretion, though many hold real-life applications. I also enjoyed the comment in the book that these chapters are organized a given manner, but that it is not the only order that makes sense for teaching or reviewing the topics of probability. The book is divided into five main divisions: General Theory, Introduction to Random Variables, Special Distributions, Limit Theorems, and Additional Topics, which includes four further topics in appendices.

The book provides a very rigorous treatment of probability using a lot of Calculus on the way. A word of warning: if the reader does not have a good understanding of Calculus, this may be quite taxing, as many descriptions given and discussed utilize integrals and derivatives. For the students that have a good understanding of Calculus, the combination of the probability discussions along with the calculus behind these topics is very beneficial for the reader.

Brent Kelderman is a high school math teacher at Millard West High School and an adjunct mathematics professor at Grace University in Omaha, Nebraska.