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. ProbabilityAxioms form the basis for mathematical ProbabilityTheory. Calculation of probabilities can often be determined using CombinaTorics or by applying the definition above directly. ProbabilityApplications include more than Statistics, which is usually based on the idea of ProbabilityDistributions.
Statistics is a branch of applied mathematics which includes planning, summarizing, and interpreting uncertain observations. ProbabilityTheory plays a critical role in the development of StatisticalTheory. We describe a universe of possible observations and the probabilities we associate with each. This allows us to plan our observations to control their variability (PlanningResearch), summarize a collection of observations to feature their communality by suppressing details (SummarizingStatisticalData), and reach consensus about what the observations tell us about the world we observe (InterpretingStatisticalData).
[The Probability Web] [Chance Database]
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