Conditional Probability
Aligned to S-CP.A.3 — Common Core State Standards for Mathematics.
What this lesson teaches
The conditional probability P(A given B) = P(A and B) / P(B) is the chance of A once B is known to have occurred. If P(A given B) = P(A), then A and B are independent.
Worked example
In a class, P(plays a sport and plays music) = 0.2 and P(plays music) = 0.5. Then P(plays a sport given plays music) = 0.2 / 0.5 = 0.4.
Practice questions
- Write the formula for P(A given B).
- If P(A and B) = 0.15 and P(B) = 0.3, find P(A given B).
- If P(A given B) = P(A), what does that tell you about the two events?
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
Probabilidad condicional
La probabilidad condicional P(A dado B) = P(A y B) / P(B) es la probabilidad de A una vez que se sabe que B ocurrió. Si P(A dado B) = P(A), entonces A y B son independientes.
Ejemplo: En una clase, P(practica un deporte y toca música) = 0.2 y P(toca música) = 0.5. Entonces P(practica un deporte dado que toca música) = 0.2 / 0.5 = 0.4.
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