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Let there be $2$ urns containing $a$ white, $b$ black balls and $c$ white, $d$ black balls respectively.Everytime a ball is drawn at random from the first urn and is transferred to the second and similarly a ball from the second urn is transferred to the first urn , both events taking place simultaneously at a particular moment.After n such operations, a ball is randomly selected from the first urn .Find the probability that it is white.

{Inspired by a problem of J.V. Uspensky}

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