Content
Course Description:
Our capacity to fathom the world around us hinges on our ability to understand unpredictable quantities. We must incorporate probability into the mix to gain more accurate mathematical models of the natural world. This course will serve as an introduction to the foundations of probability theory.
Tentative topics:
 Discrete and continuous probability distributions
 Conditional probabilities
 Bayes' formula
 Expected value and variance
 Conditional expectations
Textbook:

Introduction to Probability Models (10th edition) by Sheldon M. Ross, 2010, Elsevier.
(The course will be primarily based on this textbook.) 
Introduction to Probability (2nd edition) by Charles M. Grinstead and J. Laurie Snell, 1997, American Mathematical Society.
(You can use this book as additional reading material. I used this book in the past, and although I am not entirely happy with it anymore, it contains many illustrative examples. The book is freely available at https://chance.dartmouth.edu.)