In an urn there are $a$ azure balls and $c$ carmine balls, $ac\ne0$. To begin with, you randomly pick a ball, throw it away, and then each time you randomly pick a ball, if it has the same color with its predecessor, throw it away, otherwise put it back. Then what's the probability that the last one thrown from the urn is azure?
For instance, a possible round:
draw urn ---------------- AAACCCCC A AACCCCC C AACCCCC C AACCCC C AACCC A AACCC C AACCC A AACCC C AACCC C AACC C AAC C AA A AA A A A -
In this round, the last one thrown is an azure ball.