Two random variables are independent if the outcomes of one occur with no dependence on those of the other. Formally, $X$ and $Y$ are independent if whenever $A$ and $B$ are events containing outcomes of $X$ and $Y$, respectively, $\mathrm{Pr}(A \textrm{and} B) = \mathrm{Pr}(A) \times \mathrm{Pr}(B)$.