Three white balls, two red ball, and two black balls are distributed in
two urns A and B in such a way so that urn A contains four balls and urn B
contains three balls. At each step, we draw one ball from each urn and place
the ball drawn from urn A into urn B, and vice versa.
Let Xn denote the number of white balls in urn A after the n-th step.
Explain why the stochastic process {Xn, n = 0, 1,…} is a Markov chain and
calculate its one-step transition probability matrix.
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