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Sample space, event, outcome definitions

Short answer

Experiment: uncertain process. Outcome: single result (e.g., die shows 5). Sample space: set of all outcomes (e.g., {1,2,3,4,5,6}). Event: subset of sample space (e.g., {5,6} for >4).

Define sample space, event and outcome of an experiment with suitable example.

Experiment

An experiment is a process that gives a result which cannot be predicted with certainty. Example: throwing a die.

Outcome

An outcome is a single possible result of an experiment. Example: when a die is thrown, getting "4" is one outcome.

Sample space

The sample space (S) is the set of all possible outcomes of an experiment. Each element of S is a sample point.

  • Tossing a coin: S = {H, T}
  • Throwing a die: S = {1, 2, 3, 4, 5, 6}
  • Tossing two coins: S = {HH, HT, TH, TT}

Event

An event is any subset of the sample space, that is, a collection of one or more outcomes. It occurs when the outcome of the experiment belongs to it.

  • Simple event: contains one outcome, such as A = {4}.
  • Compound event: contains more than one outcome, such as B = {2, 4, 6} ("an even number").

Example together

Experiment: throwing a die once.

TermExample
Outcome5
Sample spaceS = {1, 2, 3, 4, 5, 6}, n(S) = 6
EventE = "number greater than 4" = {5, 6}
Probability of En(E)/n(S) = 2/6 = 1/3

✓ Answer checked by Claude Sonnet 5.5

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