A First Course in Probability [Paperback]

I rarely review items I don't find to be worthwhile, but in this case, I sense that I may have specific complaints that will help buyers with a choice to keep from making a mistake. Although this item does cover the territory, it does it in a way that doesn't leave much room for positive recommendation.

My overall impression of the book is that it's very well organized, logically develops the topic, and loses it completely in the details.

Primary drawbacks:
* very few illustrations
* teaches by example rather than exposition
* examples are lacking in that they skip steps and sometimes leave results in incomplete states.

The title of the book leads you to believe that a moderately-educated student, in any one of a number of fields including "soft sciences," could use this book to learn probability. I quote from the Preface; "This book is intended as an elementary introduction to the theory... for students in mathematics, statistics, engineering and the sciences (including... the social sciences, and management science)...." However, reality is quite a bit far afield from this ideal. If you aren't very comfortable with single- and multi-variable calculus, and don't have a course in formal logic or mathematical proof under your belt, you will find this material difficult to read and master.

Examples are initially, and throughout, extremely dense and take a great degree of mental effort to unpack. For instance, the very first example in Chapter 3 on Conditional Probability reads as follows: "A student is taking a one-hour time-limit makeup examination. Suppose the probability that the student will finish the exam in less than x hours is x/2, for all 0 <= x <= 1. Then given that the student is still working after .75 hour, what is the conditional probability that the full hour is used?" What follows is a convoluted mess of probabilities, complementary probabilities, and probability transformations that are never explained before or after this example. (All of this is to demonstrate, for example, that the odds of getting two heads on two coin flips are different when you know one of the coins already turned up heads than when you flip two coins with no knowledge of what the outcome will be. (It's 1/3 instead of 1/4, because you know that you can't possibly get two tails.)).

Having sat through a number of math classes, I understand the need for abstraction to get at the root of an idea; some of the examples take this idea of abstraction just a little too far. For example, initiated by the idea that when the author "of this text drinks iced tea... he continuously refills the tea glass with water... and wonder[s] about the probability that his final gulp would be tea." The setup for this example continues: "Urn 1 initially has n red molecules..." and continues in this vein. It goes on for a page and half, just a bit complex. The probability, in case you're wondering turns out to be about e^-1 (or 1/e). We discover this by, again, transforming half a page of equations into (1 - 1/n)^n, which I'm sure you will recall from your explorations into sequences and series is the aforementioned quantity. Although I understand that the probability that the author's last sip will NOT be tea is 1- (1/e)... of what use this knowledge is, I don't know. The author happily continues on in this vein with yet more arbitrary calculations for another half-page or so.

My second complaint about this book is that even though it's in its Eighth edition, explanations aren't clear and it seems somewhat unfinished - it seems like it may have taken its authors and editors eight editions to get it to this convoluted state. Since it is in its eighth edition, why does it cost so much? Certainly it's not the quality of the exposition that sets this book apart or ahead of the many numerous other choices available. Perhaps there's some sort of dreadful Textbook Network Effect going on, and this one's been around the longest, is the most widely used... and is now the Cash Cow of the Probability Industry.

My next complaint with this text is the lack of illustration provided that makes this a dreadful read. Although I've only read the first five chapters (of some nine we'll cover in class), but I find the lack of clarifying illustration to be a severe drawback to understanding the examples. The illustrations that are provided seem to be the most basic that the authors could get away with. Almost no energy was exerted to bring any illustration to the provided examples - and what illustration there is could be done by a first year computer science student with a Linux box and LaTeX distribution.

I will say that there are plenty of examples, but it's not well-articulated why these examples were chosen. Some seem to repeat the same point, while others seems to introduce new material in the calculations without a mention - results that are used in later examples, again without mention of their development or reinforcement in text points subsequent to the actual example.

After re-reading this book, I'm still finding glaring omissions. For instance, it is common to find the median value for a continuous distribution by setting value = 0.5 and integrating to find the value of the integral of a particular distribution. This book does not discuss this technique, nor is it even mentioned in the index.

My final complaint about the examples given is not that they skip steps - this can be good for making a student work to figure out what's going on - but that often, the examples stop short of a complete solution. Students learn partially by observation, and seeing these examples leads a student to believe "that's all there is to it," which can result in an incomplete understanding of the goal as well as poor technique on graded work.

In short, even though this book has been through numerous revisions, I cannot find much to highlight as a positive, articulate exposition of probability. It develops its topic in the same way as innumerable other books on the subject. It seems to have little to no distinguishing features (other than the cost). And given the topic, I'm quite certain you can find alternative - or supplemental - materials that will help you master this subject.

Bottom line: I am giving this text two stars rather than one because, although it's a difficult read and inappropriately marketed (who would buy a book titled "Probability for the Pedantic, with Esoteric Examples?"), it does indeed cover the topic material in a logical order and to a depth that likely will make this a good reference book. I also haven't found any typos (yet). However, the book's poor readability, lack of illustrations, and unhelpful examples detract from its other intrinsic qualities. Stay away from this book unless you are a particularly well-prepared math student.

I would recommend The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!) as a supplement if you must use the reviewed book as a text.

Let me preface this by saying that I'm basing my review on an older edition from my math major undergraduate days. I'm now working through the book for the second time after many years.

I do like this book. It's topic coverage is good. The order is logical. There are plenty of examples. However... to tell you the truth, I really don't know how I got through the class all those years ago with an A. I'm working through it now and I see some glaring weaknesses (in my opinion as a math instructor) in the book that would be quite frustrating for someone seeing this material for the first time. It's even frustrating for me on round two! I'll tell you right now, you need more "mathematical maturity" than a year of calculus, an intro to linear algebra, and an intro to differential equations will provide.

First, I do like that there are tons of examples. But I think they could have been picked and graded in difficulty a bit better. It seems to me they are a bit polar. Some are trivial, routine problems, which I do understand are necessary. But the rest are almost always the sorts of problems you can spend days pondering. The same applies to the problem sets. So you get this effect where several problems are as easy to think through and do as a routine beginning calculus or algebra problem. Then you hit this wall and a problem can take days of pondering. There really needs to be something in between. The "theoretical problems" are even worse. Almost all of them are quite complicated proofs. There needs to be some more routine proofs in there as well.

Second, Ross tends to give all those examples--which is fine--at the expense of a bit more thorough base explanation--which is not fine. There needs to be a bit more development thrown in there.

Third, the problem sets need to be broken down into smaller sets for each subsection. By the time you've read all the pages between problem sets, you've started to forget the earlier stuff before you have a chance to firm in up with some exercises.

So, overall, this book is a mixed bag. Honestly, I wouldn't want to use it at this point as an introduction if I hadn't already gone through the stuff in the past. I think there are better books out there for this. Especially for self-study. I have several and I'm now ordering one that covers the material in a smoother manner and will give me less heartburn as I review. I think my favorites at this point are "Basic Probability Theory" by Ash (it's quite terse but things are explained well) and "Introduction To Probability" by Bertsekas (this one is actually the best I've seen--got it from a library and am now ordering my own copy). By the way, I have Ross' follow up "A Second Course in Probability" and strangely enough, the weaknesses with A First Course in Probability have been addressed for the most part. But his second course is more measure theoretic, and requires a bit of familiarity with analysis along the material from his first book.

If you have a choice in the matter or you are studying on your own, I'd say buy Introduction To Probability by Bertsekas and perhaps use Ross as a supplement or as a reference (it works well for those tasks). From there, if you're really into it, you might want to tackle "Probability and Measure Theory" by Ash/Doleans-Dade.

If you do use only Ross and want to understand the material in the book, be prepared to build your own bridges across some very wide rivers. Not the kind of thing you want when you are under the time constraints of a semester.

This is a good introduction to the topic of probability, but only for mathematicians, computer scientists, physicists, engineers, and other mathematically adept people.

The book is not heavy on analysis, and does not require intensive knowledge of proofs or ability to compose proofs. The theoretical exercises are intriguing and very fun to work through. The exposition is clear and logically developed. Also, there are a variety of examples that make the topic seem even more interesting than it is. Thus, there are many reasons why this book is in its 8th edition.

Having said this, though, a caveat is that the reader needs a solid math background to appreciate it. This is not a book for a social science or even a non-mathematically adept econ student. It is possible to understand some to most of it without analysis and abstract algebra, but both are very helpful and are indispensable for appreciating the beauty of the book.

Some drawbacks are that there are no explanations, some of the counting problems are tedious and routine, and at times there is insufficient rigor. But all in all, it is a solid intro to probability - but only for the mathematically adept.