ABSTRACT
This chapter focuses on the basic results and illustrate the theory with several numerical examples. Probability theory essentially provides a framework and tools to quantify and predict the chance of occurrence of an event in the presence of uncertainties. Probability theory also provides a logical way to make decisions in situations where the outcomes are uncertain. Probability theory has widespread applications in a plethora of different fields such as financial modeling, weather prediction, and engineering. The literature on probability theory is rich and extensive. The proofs of the major results are not provided and relegated to the references. While there are many different philosophical approaches to define and derive probability theory, Kolmogorov's axiomatic approach is the most widely used. This axiomatic approach begins by defining a small number of precise axioms or postulates and then deriving the rest of the theory from these postulates.
