Some additional references:

W. Feller. An Introduction to Probability Theory and Its Applications, Vol. I, 3rd Edition. Wiley, 1968. QA273.F3727. This is the best book on elementary probability theory, is extremely well written, and contains many interesting things. If you want to learn more about random walks, begin here.

J.W. Pitman, Probability, Springer, 1993. A harder textbook than Ross, containing many interesting and challenging problems.

H. Wilf. generatingfunctionology. This is one of the best mathematics books written at an undergraduate level, and can be obtained from the author's website. Browsing this will teach you how to do many calculations very easily using generating functions. Recommended if you want to learn more about generating functions, a topic we will unfortunately treat only briefly.