In a communication system with communication tree shown below, a 3 is sent three times more frequently than a 1, and a 2 is sent two times more frequently than a 1. If we observe a 1 in the receiving end, what is the probability that 1 was sent? Consider a = 0.2, 8 = 0.4, y = 0.26 (Hint: use Bayes' Theorem) P[Y = 1 | X = 1] = 1-a X = 10 Y = 1 a/2 a/2 PLY = 2 | X = 2] = 1-B B/2 X = 20 Y =2 B/2 2/2 y/2 X= 30 Y=3 P[Y = 3 | X = 3] = 1- y