Customer Reviews

Introduction to Probability (Dover Books on Mathematics)

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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.

I've never seen a probability book with such good examples. Most books on probability give you all of the equations, but they don't really tell you how to apply them to real situations. This book has nothing but real examples. It is the book on probability that I have been looking for

This book is very good for those who have little knowledge in Probability but do manage some basic math concepts: polinomials, factorials, limits, etc. I bought it because I was looking for a mathematical course in Probability but this book is not for that, it is very simple. It is not a "definition-theorem-proof" book.

As an introduction to probability, this is an excellent book: easy to read, easy to follow, good contents, etc. The title does say introduction, so don't expect to emerge as the master of probability/statistics after reading this book.

Nice examples, a bit basic for my needs.

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

The fundamentals of probability are topics that most students pick up fairly well and also seem to enjoy. It is also a skill that is growing more essential for effective functioning in modern society. This book is designed to teach those basics and the level and quality of exposition are what they should be to get the job done. The chapters are:

*) Possibilities
*) Probabilities
*) Expectations
*) Events
*) Rules of probability
*) Conditional probabilities
*) Probability distributions
*) The law of large numbers

A large set of detailed problems appears at the end of each section and short solutions to the odd-numbered ones are included in an appendix.
If you are teaching a short course in probability or want to learn it on your own, this book will work well for you.

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.

Introduction to Probability by John E. Freund feels like an ordinary text that plays out the same just like the others I read in college. There is an attempt to explain some of the topics offered: possibilities, probabilities, combinations, permutations, conditional probabilities, Venn diagrams, Bayes' rule, and probability distributions. In short, I didn't see anything new. Also, Freund doesn't go as deep as if he wanted to, but that's understandable since it's only an introduction book. Based on the ample supply of concrete examples, I find the explanations to be fair but lacking. The end-of-the-section questions are many, and as usual, devoid of worked-out solutions in the end (you only get odd numerical answers). In my experience, the study of probability was one of the toughest undertakings that I was able to spend a lot of time over the years, getting the knack of solving questions in different forms while employing the right technique. So, I can't honestly say that my ability would be improved if I started with Introduction to Probability by John E. Freund, so I suggest you to look elsewhere. On the other hand, I would recommend this book as a suitable college textbook provided that the students will get a guided tour along with helpings of how to solve the (not that hard, really) problems offered. All in all, Introduction to Probability is not worth buying if you know the subject well enough and is not worth buying if you know squat about it.