Independent Events

Situations in which the occurrence or non-occurrence of one event has NO INFLUENCE on the next event that occurs.

Notation

$E\perp F$

Definition

$E$ and $F$ are Independent events $⟺P(F|E)=P(F)$

Formal Definition

$P(A\cap B)=P(A)P(B)$

Rules

Product Rule

For Compound Events, the product rule is: $P(A\cap B)=P(A)\ast P(B)$

• Independent Event Product Rule Proof

Union

$P(A\cup B)=P(A)+P(B)-P(A\cap B)$ Alternate to: Dependent Events

Examples

• Proving Independence