Probability is the mathematical theory we use to describe and quantify uncertainty. Uncertainty can be due to our ignorance, deliberate mixing or shuffling, or due to the essential randomness of Nature. In any case, we measure the uncertainty of events on a scale from zero (impossible events) to one (certain events or no uncertainty).
ProbabilityAxioms form the basis for mathematical ProbabilityTheory. Calculation of probabilities can often be determined using CombinaTorics or by applying the axioms directly. ProbabilityApplications include even more than Statistics, which is usually based on the idea of ProbabilityDistributions.
ProbabilityTheory plays a critical role in the development of StatisticalTheory. Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. We describe our knowledge (and ignorance) mathematically and attempt to learn more from whatever we can observe. This requires us to
There are some ScienCes which use statistics so extensively and have specialized terminology that we recognize special disciplines like: