Independence

Two events $E$ and $F$ are said to be independent if the occurrence of one of the events gives no information about the probability of the other event. $$ \boxed{p(E | F) = p(E)} \text{ or } \boxed{p(F | E) = p(F)} $$

Using conditional probability, we can obtain that $E$ and $F$ are independent events whenever $p(E\cap F)=$ $p(E) \cdot p(F)$.