There are 8 black marbles and 4 red marbles in a bag. Three marbles are to be drawn at random from the bag, without replacement. (a) Construct the probability tree for this problem. (b) Let random variable X represent the number of red marbles selected. Determine the probability distribution function for the number of red marbles selected. Show all of your calculations. (c) Determine E(X), the expected number of red marbles selected