Probability theory
Probability abstraction is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability concepts treats the concept in a rigorous mathematical variety by expressing it through a nature of axioms. Typically these axioms formalise probability in terms of a probability space, which attaches a measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any subject subset of the sample space is called an event. Central subjects in probability theory increase discrete & continuous random variables, probability distributions, and stochastic processes which dispense mathematical abstractions of non-deterministic or uncertain processes or measured quantities that may either be single occurrences or evolve over time in a random fashion. Although it is for not possible to perfectly predict random events, much can be said about their behavior. Two major results in probability theory describing such(a) behaviour are the law of large numbers and the central limit theorem.
As a mathematical foundation for statistics, probability theory is necessary to numerous human activities that involve quantitative analysis of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics or sequential estimation. A great discovery of twentieth-century physics was the probabilistic nature of physical phenomena at atomic scales, remanded in quantum mechanics.