Probability

This chapter provides a brief history of the concept of probability and Russian mathematician Andrej N. Kolmogorov's axioms of probability. These axioms are best understood by thinking of probabilities as proportions. When one views probability through the eyes of Kolmogorov, as a kind of proportion, Euler diagrams are natural tools for understanding and calculating simple probabilities. The whole, or "universe" for the probability calculations, is Ω. Subsets of the sample space Ω are then best viewed as collections of outcomes. The chapter then describes the difference between the straightforward probability and the conditional probability. It details probabilities for repeated samplings. The chapter talks about the conditional independence. Independence between any two events is that the occurrence of one of them does not influence the probability of the occurrence of the other.