Examination requirements: understand the concept of sample space (basic event space), understand the concept of random events, and master the relationship and operation of events. Understand the concepts of probability and conditional probability, master the basic properties of probability, calculate classical probability and geometric probability, and master the addition formula, subtraction formula, multiplication formula, total probability formula and Bayesian formula of probability.
Axiomatic definition
How to define probability and how to base probability theory on strict logic is a difficult point in the development of probability theory, and the exploration of this problem has been going on for three centuries. Lebesgue's theory of measurement and integration, which was completed in the early 20th century, and the abstract theory of measurement and integration, which was developed later, laid the foundation for the establishment of axiomatic system of probability theory.
Under this background, the Soviet mathematician André Andrey Kolmogorov gave the definition of the measure theory of probability and a strict axiomatic system for the first time in his book The Basis of Probability Theory 1933. His axiomatic method became the basis of modern probability theory, making it a rigorous branch of mathematics, which played a positive role in the rapid development of probability theory.