Reusability or Generalisation of a result in problem solving-2

Let us now see a problem that focus on generalisation of a result to solve a problem

Problem Description : Box A1 contains a white balls and b black balls. Box A2 has a white balls and b black balls. A ball is drawn from A1 and is transferred to A2. Now, if a ball is drawn from A2 find the probability that it is white.


Solution  :  Upon observation, we can see that the required answer can be easily obtained by the application of Bayes' Theorem as

Generalisation :
    A1, A2, A3 .... An are n boxes each containing a white balls and b black balls. A ball is transferred from A1 to A2 and then from A2 to A3 and so on such that the last transfer is from An-1 to An. Then the probability that a ball drawn from An is white is