Box A contains 8 black marbles and 5 white marbles. Box B contains 8 black marbles and 9 white marbles. A marble is randomly drawn from Box A and its color recorded. The marble is then placed in Box B and a marble is randomly drawn from Box B and its color recorded. (a) Sketch a probability tree to represent this situation. (b) Find the probability of each possible outcome. (c) Find the probability that a black marble is drawn on the second draw. (d) Find the probability that at least one of the marbles drawn is white. (e) Find the probability that the second marble is black, given the first marble is white

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