Discret Markov Chain. I have 2 boxes with N balls in each box. N of the 2N balls are white and N are black

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Let $N = 2,3,4,...$ We have 2 boxes with $N$ balls in each box. $N$ of the $2N$ balls are white and $N$ are black. In each step we take an random ball from each box and swich them around. The state is the number of white balls in the the first box.

  • I need to Find the transition probability matrix??
  • and find the state transition diagram?

How do I do that?

Thanks