Probability theory has its origins in the analysis of games of chance in the 17th century. It was placed on a solid mathematical foundation when Kolmogorov, in the early 1930s, did not concern himself with defining what probability is, but instead formulated axioms that probability satisfies and from which calculation rules and mathematical theorems can be derived. Random variables then become certain maps. I will explain this to you, as well as what the expected value and variance of random variables mean and how to calculate them.