In the third video in the series on The Basics of Probability Theory, Dr. Harvill illustrates using Kolmogorov's Axioms to develop a method for reasoning and calculating probabilities.  She first illustrates these principles on operations on sets.  Also in this video are Bonferroni's inequality, Boole's inequality, and the Law of Total Probability.  Venn diagrams are used to illustrate how to visualize these relations and their probabilities.