Multiple choice

One bag contains $3$ white & $2$ blacks and another contains $2$ white & $3$ black balls. A ball is drawn from the second bag & placed in the first, then a ball a ball is drawn from the first bag & placed in the second. when the pair of the operations is repeated, the probability that the first bag will contain $5$ white balls is:

  1. $1/25$
  2. $1/125$
  3. $1/225$
  4. $2/15$
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