Fundamental theorems in the probability theory

Probability theory is an area of mathematics that deals with the subject of likelihood. Probability theory is the mathematical cornerstone of statistical reasoning, and it is vital for data scientists to analyze data that are impacted by randomness. It is important in machine learning since the design of learning algorithms frequently relies on probabilistic data assumptions. Probability is a concept that is used to quantify the degree of uncertainty. The goal of probability theory is to express uncertain phenomena using a set of axioms. To cut a long tale short, when a system's probable outcomes cannot be certain of, mathematicians try to depict the situation by calculating the probability of various events and scenarios. Random variables, independence, entropy and Chebyshev inequality will all be discussed in this paper. These mathematical concepts and theorems are essential and fundamental for future study in other scientific areas.