In the first box, there are 4 white and 7 black balls. In the second box, there are 3 white and 6 black balls. A ball is randomly chosen from the first box and transferred to the second box, and then a ball is randomly chosen from the second box and returned to the first box.   (a) Find the probability that, after all this, we draw a white ball from the first box.   (b) If a black ball is drawn from the first box after the transfers, what is the most likely composition of the first box

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