The probability theory is a mathematical study of unpredictable events occurring in the interface of the real world with various subject areas. Informally, probability is a measure of the “likelihood” of occurrence of such an event. Our emphasis in this chapter is the discrete probability theory. We introduce some basic tools inasmuch as needed to discuss some significant probabilistic problems related to computer science. We start with basic aspects of Kolmogorov’s probability model and prove certain core results involving the expectation and variance of a random variable. The core idea is to use average behavior of problems to analyze, even when the associated distributions are not known. We conclude the chapter with some useful concentration inequalities and limit theorems.