Probability theory is a branch of mathematics concerned with the nature of randomness and the study of random phenomena. The outcome of a deterministic event can be predicted from the available information, while the outcome of a random event, by definition, cannot. Stochastic modeling is often needed when the information of a system is incomplete and the state of the system is affected by factors that are not included in the model. Since such a situation is commonly encountered in the modeling of real world phenomena, probability theory has a wide range of applications, including modeling of financial markets, atmosphere and weather, biological systems, dynamics of gases and liquids etc. Because of the intrinsic probabilistic nature of quantum physics, probability theory is also a cornerstone of modern physics.
While probability is an old field of mathematics, with roots in studying games of chance, it has grown into a large and vibrant area of research in pure and applied mathematics. Modern probability theory relies upon the axiomatic formulation of Kolmogorov, and its foundations are in measure theory. In addition to applications outside mathematics probability theory has been used as a tool for understanding problems in many areas of pure mathematics. Probability theory is the basis of statistical analysis, and understanding the fundamentals of probability is important to the study of modern computational statistics.