Trials, Outcomes, and Sample Spaces
Probability is the branch of mathematics that deals with measuring how likely events are to occur. To work with probability, we need some precise vocabulary.
Trial
A single execution of a random experiment — for example, rolling a die once or flipping a coin once.
Outcome
A specific result of a single trial — for example, rolling a 4, or getting heads.
Sample Space (U)
The set of all possible outcomes of an experiment. It is denoted by the letter .
Example
Single coin flip:
Rolling a six-sided die:
Rolling two dice: contains 36 ordered pairs, from to .
Sample spaces can be represented in several ways:
- Lists — simple enumeration, e.g.
- Tables — useful when combining two experiments (rows = one die, columns = the other)
- Tree diagrams — show sequential stages clearly
Exam Tip
Always write out the full sample space before calculating any probabilities — it stops you from accidentally missing outcomes!
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