Probability is the branch of mathematics which studies the possible outcomes of given events together with their relative likelihoods and distributions. In common usage, the word ``probability'' is used to mean the chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a Percentage between 0 and 100%. The analysis of events governed by probability is called Statistics.
There are several competing interpretations of the actual ``meaning'' of probabilities. Frequentists view probability simply as a measure of the frequency of outcomes (the more conventional interpretation), while Bayesians treat probability more subjectively as a statistical procedure which endeavors to estimate parameters of an underlying distribution based on the observed distribution.
A properly normalized function which assigns a probability ``density'' to each possible outcome within some interval is called a Probability Function, and its cumulative value (integral for a continuous distribution or sum for a discrete distribution) is called a Distribution Function.
Probabilities are defined to obey certain assumptions, called the Probability Axioms. Let a Sample Space contain
the Union () of all possible events , so
(1) 
(2) 
(3) 
(4) 
Let denote the Conditional Probability of given that has already occurred, then
(5)  
(6)  
(7)  
(8)  
(9)  
(10) 
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(12) 
See also Bayes' Formula, Conditional Probability, Distribution, Distribution Function, Likelihood, Probability Axioms, Probability Function, Probability Inequality, Statistics
© 19969 Eric W. Weisstein