Given an event
in a sample space which is either finite with elements or countably infinite with elements, then we can write
and a quantity ,
called the probability of event , is defined such that
1. .
2. .
3. Additivity: ,
where
and
are mutually exclusive.
4. Countable additivity: for , 2, ..., where , , ... are mutually exclusive (i.e., ).
See also
Experiment,
Independence Axiom,
Kolmogorov's Axioms,
Outcome,
Probability,
Sample Space,
Trial,
Union
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References
Doob, J. L. "The Development of Rigor in Mathematical Probability (1900-1950)." Amer. Math. Monthly 103, 586-595, 1996.Papoulis,
A. Probability,
Random Variables, and Stochastic Processes, 2nd ed. New York: McGraw-Hill,
pp. 26-28, 1984.Referenced on Wolfram|Alpha
Probability Axioms
Cite this as:
Weisstein, Eric W. "Probability Axioms."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ProbabilityAxioms.html
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