An urn contains 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 with another ball of same colour. The process is repeated. Find the probability that the third ball drawn is black.
I am getting the final answer as $5/8$ from my tree diagram. But in my book the answer is $23/30$. I don't know where I am going wrong. Please help.