Event (Probability)

Updated 01 Oct 2026

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Definition
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  an outcome, or a set of outcomes, of an experiment
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  formally: a subset $A$ of the universe (sample space) $U$ ; its probability is the sum of the weights of the elements in it, $\Pr[A] := \sum_{x \in A} P(x)$
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Note
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  the probability of the whole universe is 1 (since all weights sum to 1); the probability of any event lies in $[0, 1]$
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Example
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  over the universe of all 8-bit strings (256 of them), the event "the two least-significant bits are both 1" contains 64 strings, so under the uniform distribution its probability is $64/256 = 1/4$
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Set operations
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  $A\cup B$ : at least one event occurs.
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  $A\cap B$ : both occur.
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  $A^c$ : $A$ does not occur.
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Discrete probabilities
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  In a finite or countable model, an event’s probability is the sum of the probabilities of its elementary outcomes.
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  This is not a general instruction to sum individual-point probabilities for continuous distributions.
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Related
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  Probability Distribution
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  Union Bound
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  Probability
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  Experiment (Probability)

Linked references 6