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
Subject classifications
