1.7 Independence

Independence

Events $X_1,\dots ,X_n$ in the same probability space are said to be pairwise independent if for all $i\ne j$ ,
$\mathbb{P}[X_i\cap X_j]=\mathbb{P}(X_i)\cdot \mathbb{P}(X_j).$

Furthermore, the events are mutually independent if
$\mathbb{P}\left(\bigcap _{i=1}^n{X}_i\right)={\prod }_{i=1}^n\mathbb{P}(X_i).$