Suppose a pair of fair dice are continually rolled until their sum is either 2 or 7.

Let A be the event that the final roll showed a sum of 2, and let B be the event that it took 30 rolls of the dice. Do you think that B is independent of A.

Hint: Recall that independence is a symmetric relation, so that B is independent of A is equivalent to A being independent of B. Is it intuitive that A is independent of B.