We teach our students that two events $A$ and $B$ are independent if $\Pr[A\cap B] = \Pr[A]Pr[B]$. Then, we often propose exercises of the form: "Prove that these two events are independent", where the students must compute $\Pr[A]$, $\Pr[B]$ and $\Pr[A\cap B]$ and notice that the equality holds....