Can an event contain only one outcome?

Yes. Such a singleton event is common in discrete models, although its probability depends on the model.

Does 'A or B' normally include both happening?

In probability, union includes outcomes where either or both events occur unless an exclusive condition is explicitly specified.

Is a business event log the same concept?

No. A log records occurrences; probability events are sets of possible outcomes, though a condition about a log can define one.

AI Glossary / Mathematics and optimization / Beginner

Event

Definition

In probability, an event is a collection of possible outcomes to which the probability model assigns a probability. It expresses a condition that may or may not be satisfied when an experiment or process produces an outcome. Examples include a delivery arriving late or a model's prediction being correct. This mathematical meaning differs from a timestamped occurrence in an event log or a business event stream.

What it means

A sample space lists the possible outcomes at the level of detail required by the model. An event selects some of those outcomes. If the realized outcome belongs to that selection, the event occurs. A single event can contain many possible outcomes: 'delivery takes more than three days' includes every allowed outcome meeting that condition. For continuous or more abstract spaces, events must belong to the specified collection of measurable sets so their probabilities are defined. In a finite elementary model, every subset can usually be treated as an event.

How it works

Define the sample space and the probability assigned to its outcomes or measurable subsets. Specify an event as a set or condition. Combine events using intersection for 'and', union for 'or', and complement for 'not'. Probabilities obey consistent rules: the entire sample space has probability 1, the empty event has probability 0, and disjoint events have additive probabilities. When events overlap, P(A or B) = P(A) + P(B) − P(A and B). Conditional probability changes the reference to outcomes satisfying a given condition, provided that conditioning event has positive probability in the elementary formula.

Three practical examples

A classifier evaluation can define A as 'the prediction is incorrect' and estimate its frequency over a specified test sample.
An operations analysis can define B as 'a request waits more than five minutes' and examine that event within particular service periods.
A quality-control model can define a joint event such as 'an item fails inspection and came from line 2', making the denominator and the combined conditions explicit.

Think of it this way

Think of a checklist that marks which possible outcomes satisfy a question. The marked collection is the event, while the actual outcome is the item that eventually appears. This analogy explains membership, but it does not assign probabilities by itself. Counting marked outcomes works only when the underlying outcomes are equally likely or when their probabilities are otherwise accounted for.

Worked example

Consider a deliberately simplified experiment with four equally likely outcomes: a request is either short or long, and its route is either A or B. The sample space is {short-A, short-B, long-A, long-B}. Let L be the event 'long request' and B be the event 'route B'. Each contains two outcomes, so P(L) = P(B) = 1/2. Their intersection contains only long-B, giving P(L and B) = 1/4. Their union contains short-B, long-A and long-B, so P(L or B) = 3/4, matching 1/2 + 1/2 − 1/4. Also P(L given B) = (1/4)/(1/2) = 1/2. In this constructed model, L and B are independent because the intersection probability equals the product of their probabilities. They are not mutually exclusive, because long-B satisfies both. Now suppose the four outcomes instead have probabilities 0.4, 0.1, 0.1 and 0.4 in the same order. The marginal probabilities remain 1/2, but the intersection becomes 0.4 and P(L given B) becomes 0.8. The labels alone do not establish independence; the probability model determines it.

Illustrative case study

In a fictional dashboard project, Meadow Service defines an event called 'late completion' before reporting a rate. Analysts specify the deadline, the population of requests, the treatment of unfinished cases and the observation period. A reviewer discovers that another report uses a different deadline and therefore a different event despite sharing the same label. The team reconciles the definitions before comparing results. The case illustrates clear measurement, not a claim that the service met an invented target.

Common misconceptions and mistakes

An event is not the same as a random variable: the variable maps outcomes to values, while an event can be defined by a condition on those values. Independence is not the same as mutual exclusivity. Two events with positive probabilities cannot be both independent and mutually exclusive. A probability of zero does not universally mean logical impossibility; an exact point can have probability zero under a continuous distribution. An observed frequency is also not automatically the true probability for every future setting, especially when sampling or operating conditions change.

Business use

When building a business metric, define the event in operational terms that another analyst can reproduce. Identify the population, time window and denominator. Distinguish unconditional rates from rates within a subgroup. Preserve overlap rules when combining alerts or categories so counts are not added twice. If the probability is estimated from data, report its sampling basis and relevant uncertainty. For a predictive model, check that the event used for training labels matches the event users believe the output describes. Small wording differences can create materially different targets.

Check your understanding

In the equally likely worked model, are 'long request' and 'route B' mutually exclusive?

Answer: No. The long-B outcome belongs to both. They are independent in that model, which is a different property.

Related terms

Learn next

draw the two worked events as overlapping sets and assign the stated probabilities to their four regions. Recalculate the conditional probabilities under the unequal model. Then write a precise event definition for one metric you use and identify what belongs in its denominator.

Sources

Sources: Jung and colleagues, The Aalto Dictionary of Machine Learning, event, sample space and probability-space notation, https://aaltodictionaryofml.github.io/ADictML_Main.pdf . The request-route experiment, probability calculations and fictional dashboard review are original educational examples. The entry explicitly distinguishes probability events from logged occurrences.

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