CurriculumGrade 12Mathematics

Independent Events

Aligned to S-CP.A.2 — Common Core State Standards for Mathematics.

What this lesson teaches

Two events are independent when one occurring does not change the probability of the other. Test independence by checking whether P(A and B) = P(A) × P(B).

Worked example

Flip a coin with P(heads) = 1/2 and roll a die with P(six) = 1/6. Here P(heads and six) = 1/2 × 1/6 = 1/12, which equals the product of the probabilities, so the two events are independent.

Practice questions

  1. Are two separate coin flips independent?
  2. If P(A) = 0.4, P(B) = 0.5, and A and B are independent, find P(A and B).
  3. P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.2. Are A and B independent?

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En español

Eventos independientes

Dos eventos son independientes cuando el que ocurra uno no cambia la probabilidad del otro. Prueba la independencia comprobando si P(A y B) = P(A) × P(B).

Ejemplo: Lanza una moneda con P(cara) = 1/2 y un dado con P(seis) = 1/6. Aquí P(cara y seis) = 1/2 × 1/6 = 1/12, que es igual al producto de las probabilidades, así que los dos eventos son independientes.

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.5Events, Unions, and ComplementsS-CP.A.1

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