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What book do you recommend for self-study of probability theory?

I have a rather significant gap in that area (in lame terms sometimes I feel I don't get it) and need to try (strugle more likely) to rectify this.

What would you recommend for someone like me, who has problem/gap in this area, would be a self-study and would not be a "heavy/scary" book or tutorial?

I assume there are such books available?

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I would recommend Pitmans "Probability". –  utdiscant Feb 11 '12 at 11:50
    
I suggest you get a quick read on "Counting Techniques" and "Set Theory Basics" topics in a Finite Math (for business) type of book before you study probability. It would help a lot. –  Emmad Kareem Feb 11 '12 at 12:36
    
@EmmadKareem:Why these topics?Are they prerequisite?In what way?Would it be possible to elaborate on this in an answer perhaps? –  Jim Feb 11 '12 at 18:00
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2 Answers

It would help if you gave a little bit of background about yourself and your goals. Are you a math major or do you have some "mathematical sophistication?" Are you interested in learning probability for its own sake or for applications?

I taught probability to undergraduate math majors recently and I used Chung's "Elementary Probability Theory." (You can check out the webpage for my course if you like.) I really like this book as a very gentle introduction to probability. Chung has a nice way of explaining the fundamental concepts in an intuitive yet rigorous manner. Also, this book has answers to many of the exercises in the back, which could be helpful for self-study, in case you get stuck. I don't believe there is a solutions manual, however. Also, I'm afraid some of my students were not very happy with the textbook (though that's typical no matter what book is used).

Alternatively, "A First Course in Probability" by Sheldon Ross is an excellent introductory level textbook, with MANY examples to help you develop your intuition. If I were in your shoes, I would probably get myself a copy of Ross's book and then follow the syllabus of the MIT course based on this book here:

http://ocw.mit.edu/courses/mathematics/18-440-probability-and-random-variables-spring-2011/

I believe there is also a solutions manual available for this book, though you may have trouble getting ahold of it if you are not an instructor.

There are also many online resources. For example http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/book.html

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I will check out these books thank you.One question though:from my experience (correct me here) topics that have other subjects as prerequisites are presented in the books as "refreshers chapters" and you don't really learn the material from there.You have to actually get another book since most of the intuitive explanation is assumed to be known or left out as "out of scope" for this book.I was wondering is this the same with Chung's book on counting and Sets? –  Jim Feb 12 '12 at 14:52
    
@Jim It seems to me that Chung's chapters on sets and counting are self-contained. However, it's hard for me to speak objectively about this, since I knew the subject before I ever opened Chung's book. I will say that one reason I chose Chung to teach from was because it was one of the only books to devote an entire chapter to sets. Also note: Chung calls the chapter "Set" -- not "Set Theory" -- probably to make it clear that this is not hard-core set theory. Rather, he just covers the very basics that you need for probability. So, yes, I think it's very elementary and self-contained. –  William DeMeo Feb 15 '12 at 5:05
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I wrote this answer based on the request of @Jim.

I suggest, based on my experience when I was a student, that you get a quick read on "Counting Techniques" and "Set Theory Basics" topics in a Finite Math (for business) type of book before you study probability. It would help a lot.

Counting Techniques are important in solving probability problems based on counting. For example, what is the probability of getting a 1 when you throw a dice twice or what is the probability of pulling a number such as 123 form a list of random numbers. The knowledge of how to calculate combinations and permutations was poorly described in many of the probability books I used for study. Discrete Mathematics texts usually offer good presentation of Binomial theorem and the understanding of the properties of the Binomial coefficient is crucial for discrete counting techniques.

Elementary set theory (set definition, union, intersection, Venn diagrams, etc.) gives a good background to understanding more about sample space construction. However, is is less important than counting techniques.

I hope this helps.

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I agree with your view that elementary set theory and counting techniques are critical for solving probability problems. This is one of the main reasons I chose Chung's book (mentioned in my answer above). Chapter 1 is called "Set." Chapter 3 is called "Counting." –  William DeMeo Feb 12 '12 at 1:13
    
@williamdemeo, thank you for your comment. I must take a look at this book. I was not familiar with it before. –  Emmad Kareem Feb 12 '12 at 4:54
    
@Emmad Kareem:Do you have a recomended book on these topics? –  Jim Feb 12 '12 at 11:32
    
@Jim, I really can't name a specific book that I have used my self. williamdemeo has already suggested one book that covers these topics. What I would do before buying a books is to check Google Books first and do some search for tutorials on the subject. Also, check sites such as: coursehero.org/lecture/introduction-probability-and-counting and oedb.org/library/beginning-online-learning/… first to get an idea before you pay for a book. –  Emmad Kareem Feb 12 '12 at 11:44
    
@Emmad Kareem:I will checkout the book mentioned by William Demeo of course.It is just that from my experience (correct me here) topics that have other subjects as prerequisites are presented in the books as "refreshers" and you don't really learn the material from there. –  Jim Feb 12 '12 at 14:50
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