Self-study on probability. 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?
 A: 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.
A: 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
