Question

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 along with another ball of the same colour. The process is repeated. Find the probability that the third ball drawn is black.

Answer 1

There are 4 possible path go get Black ball in 3rd draw :

BBB , BWB , WBB & WWB

Probablity is 12×12×12 + 12×12×23 + 12×23×23 + 12×13×1 = 4972