Finite probability spaces

This lecture covers the definition of a finite probability space as a pair (Ω, P) where Ω is a finite set and P is a function assigning numbers in [0,1] to every subset of Ω. It introduces the concept of probability theory to set theory, explaining elementary events, events, and examples of finite probability spaces. The lecture also discusses random permutations, random graphs, and random trees, illustrating the properties and calculations involved in each case.