CurriculumGrade 12Mathematics

Events, Unions, and Complements

Aligned to S-CP.A.1 — Common Core State Standards for Mathematics.

What this lesson teaches

The sample space is the set of all possible outcomes, and an event is a subset of it. Combine events using union (A or B), intersection (A and B), and complement (not A).

Worked example

Roll a die, so the sample space is {1, 2, 3, 4, 5, 6}. Let A = even = {2, 4, 6} and B = greater than 3 = {4, 5, 6}. Then A and B = {4, 6}, A or B = {2, 4, 5, 6}, and the complement of A is {1, 3, 5}.

Practice questions

  1. List the sample space for flipping two coins.
  2. For a die roll, list the event "less than 3."
  3. If A = {1, 2, 3} on a die, list the complement of A.

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En español

Eventos, uniones y complementos

El espacio muestral es el conjunto de todos los resultados posibles, y un evento es un subconjunto de él. Combina eventos usando la unión (A o B), la intersección (A y B) y el complemento (no A).

Ejemplo: Lanza un dado, así que el espacio muestral es {1, 2, 3, 4, 5, 6}. Sea A = par = {2, 4, 6} y B = mayor que 3 = {4, 5, 6}. Entonces A y B = {4, 6}, A o B = {2, 4, 5, 6}, y el complemento de A es {1, 3, 5}.

More Statistics & Probability lessons

Making Inferences from SamplesS-IC.B.4Normal Distributions and the Empirical RuleS-ID.A.4Making Inferences from SamplesS-IC.A.1Surveys, Experiments, and Observational StudiesS-IC.B.3Comparing Two TreatmentsS-IC.B.5Independent EventsS-CP.A.2

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