TITLE: Self-study on probability.
QUESTION [9 upvotes]: 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?

REPLY [4 votes]: 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.