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Rating: 
Summary: A Classic of Probability Theory
Review: A First Course in Probability by Sheldon Ross covers all the main topics of probability theory: Combinatorics, Probability Axioms, Conditional Probability and Independence, Discrete Random Variables, Continuous Random Variables, Joint Distributions, Expectation, and Limit Theorems. He develops each topic thoroughly using the definition-theorem-proof approach of classical mathematics, interspersed with numerous examples, many of which are classics in probability.
This book does require a solid foundation in calculus. Consequently, it is an appropriate text for a course at an advanced undergraduate level or even a first year graduate course (which is where I first encountered it). It does not require any knowledge of truly advanced mathematics (i.e., measure theory) which one would expect to find in an upper level graduate text, such as Patrick Billingsley's Probability and Measure.
Advice to students (and teachers): A student who does not have a solid foundation in calculus, as evidenced by the ability to apply integration by parts, and perhaps a year of post-calculus math which introduced the concept of the mathematical proof, will have a difficult time with this book.
This book provided me with all the probability theory I needed to complete a master's degree in statistics. Since statistics is nothing more than a collection of applied problems that can be solved, modeled, or at least understood by using the tools of probability theory, I was able to coast through the rest of my master's program and didn't have to start really working again until I subsequently encountered Billingsley's book (cited above).
Thank you, Professor Ross.
Rating:
Summary: One of the best books on the subject
Review: Although it's titled "a first course", the reader will find difficulty in using the book without a background in Cal II. This book is clear, concise, with lots of inspiring examples to expound the concepts & applications. It would be wonderful if a solution manual were written, however. The exercises are well written and some challenging, and if no sufficient practice has been done to comprehend the concepts in the chapter, the reader is likely to stumble on the exercises. If you enjoy exploring the mathematical reasoning behind the applications, have the necessary prerequisites (calculus) and are willing to pay the efforts, this book is a great choice.
Rating: 
Summary: confusing and badly organized
Review: avoid at all costs. important equations lost in irrelevant text. problems not divided by section and examples don't reflect the material in problems. Many proofs and explanations skip steps and assume much. solution manual needed but unavailable. good luck if stuck with - don't buy if don't have too!!
Rating:
Summary: Un-pleasant
Review: I just finished up taking a Probaility course which utilized this book. Over-all I found this book to be terrible and even our Professor had some guarded comments about the quality of the book.
The first few chapters ( 1-4) are straight foward but once i got to chapters 5,6 and 7 I felt like the author was simply rushing through the material in order to get it published as soon as possible. The examples are so so and the author skips large numbers of steps in almost all of the examples. This books assumes you know probablity, it does not teach it. I also felt that for the price ($100) the author could have spent more time in chapter 6 and 7 working through all the material in greater detail. I ended up buying 2 additonal Stat/Probability books to find additional information. I have yet to find a good comprehensive book on the subject, but I am still looking. I have heard that Ross has a monopoly on probaility book and I'm not sure why but I and my fellow students were not happy about that fact. Hope this helps.
Rating: 
Summary: Better than the average math book
Review: I used this book in an intro. probability course and was pleasantly surprised with it. Most math books I have used in the past have either been too sparse on worked examples, or too wordily confusing in the presentation. This book was nice in that it contains two types of exercises (normal and theoretical) as well as Self-Test problems that have detailed answers in the back. Those self-tests really help when preparing for exams. Content-wise, the explanations were fairly clear and straight-forward with a lot of real-world examples. As far as math books go, this is better than the norm.
Rating:
Summary: Better than the average math book
Review: I used this book in an intro. probability course and was pleasantly surprised with it. Most math books I have used in the past have either been too sparse on worked examples, or too wordily confusing in the presentation. This book was nice in that it contains two types of exercises (normal and theoretical) as well as Self-Test problems that have detailed answers in the back. Those self-tests really help when preparing for exams. Content-wise, the explanations were fairly clear and straight-forward with a lot of real-world examples. As far as math books go, this is better than the norm.
Rating:
Summary: Be careful about what other people say
Review: I've almost did not bought this book because of other complains.
Those guys who complain about this book probably don't have enough knowledge to appreciate this book and should firt criticize themselves instead of crying because did not fully understand what a PhD form Stanford wrote. This book has really interesting worked examples and hard exercicies. It is true that it need a solution manual, but there are plenty of worked solution for some kind of problems. Anyway, if you never undertood very well combinatorial analysis and probability in high school, you rather buy some other book.
Rating:
Summary: A good read with lots of examples
Review: This is a fantastic text that is aimed at those who are interested in applications and not theory. The book is loaded with examples most of which have detailed solutions that are clear and easy to understand. I must stress that this book is very light on theory (though each chapter contains difficult "theoretical exercises"), and is not a sufficient text for anything but an introductory course.
Rating:
Summary: extremely unhelpful
Review: This is not the worst textbook I've ever used, but it's far from the best. Whichever reviewer was complaining about important things not being in boxes is right. One example which sticks out in my mind is as follows. In section 7.6 Ross explains moment generating functions, but nowhere in the section is there a definition of moment. Consequently, I never really understood moment generating functions, and there was a final exam question on them in the course I took. Well, if you happen to know that the first moment is the same as the mean, then you might for some reason look up "first moment" in the index (don't bother looking for "moment", because it's not there). The entry for "first moment" says, "see mean". Then if you look up "mean", you'll find that in section 4.4 on the Expectation of a Function of a Random Variable, there is, in fact, a tiny prose blurb which defines moment. No boxes, no nothing. It's just three lines between a proof and the next section. I guess this is fine for people with photographic memory and perfect recall. Also, the examples were numerous, and tended toward the elaborate, which clutters the text. I think the author intended to make things stick better by using examples he thought would be easy to recall. Personally, I've gotten used to the more common math pedagogical model of defintions, theorem, proof, which is more or less disposed of in this text in favor of extensive examples. Or maybe it just seems that way because the examples drown everything else out. In general, I felt this text could benefit from more formalism and fewer examples. When the author writes something, he should think to himself, "Have I defined all of the terms in this statement? If so, is the reader likely to remember them, or can they easily be looked up?" I don't think Ross was asking himself these questions as he wrote this book.
Rating:
Summary: Overall a pretty good text.
Review: Well first off I would like to tell anyone who doesn't have a solid working knowledge of calculus (including multivariate) to avoid this book as it requires multiple integrals and infinite series and sequences. Now onto the good and the bad:
THE GOOD:
This text explains concepts very well and is FULL of examples. I mean literally 3/4 of the book, maybe more, is examples. Every chapter also has a section of problems that have partial solutions, which can come in very handy. This is pretty much all that is good about this text, but keep in mind that explaination is the most important part of any textbook.
THE BAD:
The proofs skip plenty of steps. And I mean plenty, so much that a proof in the book would take 5 lines but when my professor proved it in class it would take him nearly 15. Also while there are tonnes of examples, too many are theoretical and very hard. I took this course first term of my second year, and it's too much to ask from second year students to solve these kinds of questions. Also there are lots of homework questions, however no solution manual, only the very few solved in the back of the book (which is better than nothing I suppose). The book also costs a hefty amount of change and is suprisingly small, not even an inch thick. However the worst thing about this book is how the author leaves important things in with the text often. Often key terms and formulae lie within the text, and are made to not look important at all (so go to class to see what's stressed!). However most these things are small, and overall the text is a good intro to probability theory.
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