p(x, y) is the probability of picking an x-colored ball on the first draw and a y-colored ball on the second draw, given that the initial ball is not replaced.For the first draw, the probability of selecting an x-colored ball is Px, and the probability of selecting a y-colored ball on the second draw is Py given that the initial ball was removed. We assume that the balls are uniformly distributed, and that Px + Py = 1. We have two possible scenarios for the order in which the balls are drawn: one in which the balls are drawn in order, and one in which the balls are drawn in reverse order.In the first situation, we may express the likelihood of this sequence of events as the product of the probabilities of each individual event, i.e.,Px * Py, whereas in the second situation, the likelihood of this sequence of events is Py * Px. We must account for both circumstances in order to determine the total probability of getting x-colored ball on the first draw and a y-colored ball on the second draw.So, the probability of obtaining an x-colored ball on the first draw and a y-colored ball on the second draw is as follows:P(x,y)=Px*Py+Py*Px=P(x,y)=2Px*PyGiven that the balls are uniformly distributed, Px + Py = 1.Thus, the probability for each outcome of the experiment is given as:P(1,1) = 2 (1/2)2 = 1/2P(1,2) = 2 (1/2)(1/2) = 1/2P(2,1) = 2 (1/2)(1/2) = 1/2P(2,2) = 2 (1/2)2 = 1/2