A good book for Probability?
I would highly recommend A First Course in Probability by Sheldon Ross.
From the hyperlinked Amazon page:
A First Course in Probability features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
I am recommending this book because I think it is suitable for self-study, as it is listed as a textbook for the Society of Actuaries' Exam P.
You can also try checking out the following books:
Mathematical Statistics with Applications by Dennis Wackerly, William Mendenhall and Richard L. Scheaffer
Probability and Statistical Inference by Robert V. Hogg, Elliot Tanis and Dale Zimmerman
Probability and Statistics with Applications: A Problem Solving Text by Leonard A. Asimow and Mark M. Maxwell