Question: An urn initially contains b black and w white balls. At each stage, we add r black balls and then withdraw, at random, r balls

An urn initially contains b black and w white balls. At each stage, we add r black balls and then withdraw, at random, r balls from the b + w + r balls in the urn. Show that
E[number of white balls after stage t] = (b + w / b + w + r)t w

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