1. Consider a binary communications channel shown in the figure below. input output 0 91 0 1 - q1 1 1 - 92 The input is 0 with probability p and 1 with probability 1 -p. When input is 0, the output is 0 with probability q, and 1 with probability 1 -q1. The corresponding probabilities are q2 and 1 - q2, respectively, when the input is 1. (a) Find the probability that the output is 0. (b) Find the probability that the input was 0 given that the output is 1. (c) Find the probability that the input was 1 given that the output is 1. (d) If the output is 1, which input is more probable? Explain