Equally likely outcomes are distinct results in a finite sample space that each have the same chance of occurring, as with the faces of a fair die or equally sized regions of a fair spinner. This understanding distinguishes a single outcome from an event containing several outcomes and supports counting-based probability; outcomes are not equally likely merely because they are listed, and conditional or nonuniform probability models are beyond this scope.
An outcome is one possible result of an experiment. Outcomes are equally likely when each one has the same chance of happening.
Look for information that makes the chances the same, such as a fair die or a spinner with equally sized sections. Simply listing results does not make them equally likely.
A fair six-sided die is rolled. Are the outcomes equally likely?
Step 1: List the sample space.
The possible outcomes are
Step 2: Check the chances.
Because the die is fair, each face has the same chance of landing face up:
Step 3: State the conclusion.
The six individual outcomes—rolling a , , , , , or —are equally likely.
Be careful: “rolling an even number” is not one outcome. It is an event containing three outcomes:
The individual outcomes are what we compare when deciding whether outcomes are equally likely.
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