Four identical urns each contain three balls. In urn I, all 3 balls are black, in urn II, 2 black and 1 is white, in urn III, 1 is black and 2 are white, and in urn IV, all 3 are white. One of the urns is picked at random, and a ball is chosen from that urn, which turns out to be white. (a) What is the probability that all 3 balls in the selected urn are white? (b) A second ball is picked from the selected urn and is also found to be white. Now, what is the probability that all 3 balls in the selected are white?

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