I wanted to ask if anyone has any recommendations for probability calculus companion books. What I mean by companion books is essentially a read-a-long to be read in conjunction with something else to help further explain it. I don't mind if the recommendation is attached to another specific book, as long as I can get what I need from it.

Long story short, I am working on a small project and I think that probability calculus is a good path to take at this point (and my curiosity is peaked as to whether or not probability calculus can be applied to it). I also do not know much about it outside of college-level mathematical number theory.

Here are the criteria I am looking for;

1) Does not deal largely with relative frequency theory. Although I appreciate number theory and realize how close it is to classical interpretive theory (probability of events, etc.), I need something... well... dumber. LOL! Seriously though, I need something that falls more into line with Propositional, Predicate, etc.

2) Deals with logical interpretive theory; hopefully, building on formal inductive logic, deals with statistical syllogisms, Mill's Method, etc.

3) Can deal with classical interpretive theory.

4) Adhere to Kolmogorov's axioms.

5) Contain sample problems and solutions (which I really really need).

Any recommendations would be greatly appreciated (preferably books rather than links...unless the links are verified). I already bought one Schaum outline book that had a few scant pages on it, but because it is a bare-bone introductory book, I need more elaborations (and sample problems).