Sometimes we use the concept of conditional independence. The definition is as follows:

let A,B,C be three events with positive probabilities. Then A and B are conditionally independent given C if P[A\B jC] Æ P[A jC]P[B jC]. Consider the experiment of tossing two dice. Let A Æ {First die is 6}, B Æ {Second die is 6}, and C Æ {Both dice are the same}. Show that A and B are independent (unconditionally), but A and B are dependent given C.