Independence of Events

Probability · Axiom Academy

When knowing one event tells us nothing about another Independence means that knowing whether event B occurred doesn't change our assessment of the probability of event A. The events don't influence each other. Events A and B are independent if and only if P(A∩B) = P(A)·P(B). This single equation captures the essence of independence: joint probability factors into a product. If P(A) > 0 and P(B) > 0, independence is equivalent to P(A|B) = P(A) or P(B|A) = P(B). Each form expresses that conditioning doesn't change probabilities. To verify independence, check if P(A∩B) = P(A)·P(B). If this equation holds, the events are independent. If not, they are dependent. This is often easier than checking conditional probabilities.

This is the written version of the interactive lesson above. See the full Probability course.