Introduction to Probability (Dover Books on Advanced Mathematics)

The target audience of this book would be 1st year undergradate students. Mathematically very simple, but everything is explained well.


Provides the reader with an understanding of basic probability.   July 7, 2007
N. F. Taussig (Bronx, NY)
6 out of 6 found this review helpful

Freund's text, which is based on a course that the author taught to university students fulfilling their general education requirement, is a clearly written and carefully constructed introduction to basic discrete probability. Each topic is placed in context and is illustrated by copious examples that demonstrate both the relevance and utility of probability. The exercises at the end of each section, which are generally straightforward applications of the material covered in that section, reinforce the reader's understanding of the material. Answers are provided to the odd-numbered exercises, making the text suitable for self-study. This text is a good entry point to the study of probability. However, the scope of the text is limited. The emphasis is on how to solve problems rather than the underlying theory. Freund succeeds in making the text as widely accessible as possible, albeit at the expense of a deeper understanding of the material.

The text begins with a chapter on enumerative combinatorics that covers tree diagrams, the Multiplication Principle, factorials, permutations, combinations, and indistinguishable objects. Freund then introduces the classical, frequentist, and subjective (Bayesian) approaches to probability. He contrasts the different approaches, demonstrates how each is applied, discusses their limitations, and shows that they lead to equivalent results. In the following chapter on the mathematical expectation of an event, Freund illustrates how probability is used in making business decisions. Next, Freund puts probability on a formal footing, discussing events, sample spaces, compound events, mutually exclusive events, and probability measures. Freund then discusses conditional probability and independent events, demonstrating how to calculate the posterior probability that a known effect had a particular cause. The remainder of the text is devoted to probability functions. The binomial, hypergeometric, geometric, and multinomial distributions are introduced, as are the concepts of mean, variance, and standard of deviation. The text culminates with Chebyshev's Theorem about the probability that a random variable will assume a value within k standard deviations of the mean and the Law of Large Numbers, which states that for a binomial distribution that if the number of trials is sufficiently large, then the number of successes will be very close to the probability of success for an individual trial.

The text is carefully sequenced so that the foundation for each new topic is covered in the preceding sections. Preceding examples are often referenced in the discussion; exercises often refer to the preceding examples, exercises, or the results of those exercises. Consequently, while the text does an effective job of teaching you the material, it does not work well as a reference.

Freund includes tables of factorials, binomial coefficients, binomial probabilities, and square roots. The presence of the last table is indicative of how old the book is. It was written before hand-held calculators came into widespread use. Reading the examples in the text will give you some idea of how much society has changed since the book was first published in 1973.

Working through Samuel Goldberg's text Probability: An Introduction after, or instead of, reading Freund's text would enable you to delve deeper into the subject. Goldberg places a greater emphasis on probability theory and proof, provides more robust examples, and challenges the reader to solve non-routine exercises.




Hardly an introduction....   April 27, 2000
Andrew Harbick (Harrisonburg, VA)
26 out of 38 found this review helpful

I'm a software developer, and have more than an avocational interest in probability. I wanted to get into the discipline proper and try to learn about probability as if I were a student in college again. This book reads like wading through waist deep bubble gum. I had to read the first couple pages about 10 times before I really understood what was going on. This book may be a good "Introduction" if you've already got a degree in math or statistics, but if you want to learn about probability from the ground up, start somewhere else.