Combinatorics and Probabilities

Probability deals with predicting the likelihood of future events, while statistics involves the analysis of the frequency of past events. Without these two fields, it would neither be possible to characterize nor to understand datasets or certain machine learning algorithms (e.g., Bayesian methods strongly rely on conditional probabilities). To count events, to create combinations of events, and to compute the probability of occurrence of particular events are important prerequisites for probability and statistics. Therefore, in Sect. 5.1, we start by introducing the foundations of combinatorics together with the most important mathematical formulations. We will then continue with deriving and computing probabilities (Sect. 5.2) using discrete and continuous random variables (Sect. 6.1 ).