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Problems dealing with various probabilities, be it coin tossing or game winning.
From bag A containing 4 black and 8 blue marbles, 6 marbles are transferred into an empty bag B. Three marbles are now drawn from bag B, and each of them happens to be black.
Determine the probability that a fourth marble drawn from bag B will be black, given that:
(I) The first three marbles are returned to bag B.
(II) None of the first three marbles is returned to bag B.
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