The goals of this chapter are to familiarize students with the concepts of probabilities and statistics to understand physical chemical principles and to analyze complex problems in chemical and biothermodynamics. The first part of the chapter will focus on events, outcomes, and their combinations. We will develop the concept of the probability distribution as a collection of probabilities for all possible outcomes. We will emphasize the differences between specific sequences of elementary events, and collections composed of specific sequences that share some overall property. This distinction is essential to statistical thermodynamics, where we are often limited to measurements of overall composition, where each composition is consistent with many different arrangements of molecules. The “indistinguishability” of these different arrangements is directly related to important thermodynamic concepts such as entropy.