Outcome (Probability)
Statistics & ProbabilityAn outcome is a single possible result of a probability experiment.
Definition
An outcome is one specific result that can happen in an experiment. When you flip a coin, the possible outcomes are "heads" and "tails."
Example
Rolling a single die has $6$ possible outcomes: $1$, $2$, $3$, $4$, $5$, or $6$. Each time you roll, exactly one of these outcomes occurs.
Key Insight
Outcomes are the individual possibilities. Events are made up of one or more outcomes. Knowing the outcomes helps you list the sample space and calculate probabilities.
Definition
An outcome is one specific result of a probability experiment, representing an element of the sample space. Outcomes are mutually exclusive (only one can occur per trial) and collectively exhaustive (one must occur). For equally likely outcomes, $P(\text{each outcome}) = 1/n$, where $n$ is the total number of outcomes.
Example
Drawing one card from a standard $52$-card deck: each of the $52$ cards is a distinct outcome. Each has probability $1/52$. The event "draw an ace" is the set of $4$ outcomes: {Ace of spades, Ace of hearts, Ace of diamonds, Ace of clubs}.
Key Insight
When outcomes are not equally likely (e.g., a weighted die), you cannot use the simple counting formula. Instead, assign probabilities directly to each outcome and ensure they sum to 1.
Definition
An outcome is an element $\omega$ in the sample space $\Omega$. In Kolmogorov's framework, individual outcomes are not always events (measurable sets), depending on whether $\{\omega\}$ belongs to the sigma-algebra $\mathcal{F}$. For discrete spaces, every singleton is an event; for continuous spaces, singletons are events with measure zero.
Example
In a probability model for a Poisson process, each outcome is an infinite sequence of event times $\{t_1, t_2, t_3, \ldots\}$. The sample space $\Omega$ is the set of all such sequences, and events are measurable subsets of these sequences (e.g., "at least $3$ events in $[0,1]$").
Key Insight
The distinction between outcomes and events is crucial for continuous probability: we can ask for the probability of a range of outcomes (an interval) but not a single real-valued outcome, because $P(\{x\}) = 0$ for any $x$.