Urn I Contains 3 Black Balls, 2 White Balls, and a Red

Short Answer

Urn I contains 3 black balls, 2 white balls, and a red ball. Urn II contains 5 black balls, 3 white balls, and 6 red balls. Urn III contains 4 black balls, 3 white balls, and 3 red balls. An urn is selected at random, one of the balls is removed randomly, observed to be white and not replaced. If another ball is then selected at random from the same urn, what is the probability it is black?