# Balls and Urns!

**Discrete Mathematics**Level 5

An urn contains\(\text{ 2 white and 2 black}\) balls. A ball is drawn at random. If it is white, it is not replaced into the urn, otherwise, it is replaced along with another ball of the same color. This process is repeated. The probability that the \(\text{third}\) ball is drawn black is of the form \[\frac { \sqrt { a } }{ b }\] ,where \(a\) and \(b\) are integers Find \(a+b\)