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
- Are two separate coin flips independent?
- If P(A) = 0.4, P(B) = 0.5, and A and B are independent, find P(A and B).
- P(A) = 0.3, P(B) = 0.6, and P(A and B) = 0.2. Are A and B independent?
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn 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.
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