## ABSTRACT

Probability theory provides the tools necessary to quantify notions of uncertainty and random variability. This chapter explores some basics of probability theory in the context of cyber research. Fundamental concepts such as sample spaces, events, probability axioms, and conditional probability are introduced. The notion of a random variable is discussed, and details of several widely used discrete and continuous random variables are presented, including probability distribution functions for each. Modeling applications and illustrating cyber-related examples are provided for many of these distributions. Expectation and variance are defined and briefly explained. The chapter concludes with an overview of some probability models used in cyber research, including ideas such as Bayes Rule, Markov chains, and information entropy. Each of these ideas is accompanied by relevant examples pertaining to various risks in the cyber domain. References for further study are suggested, and appendices are included with summary tables of important distributions and Normal distribution probabilities.