In the ternary communication channel shown in Figure P1.32 a 3 is sent three times more frequently than a 1, and a 2 is sent two times more frequently than a 1. A 1 is observed: what is the conditional probability that a 1 was sent?

X= 10 a/2 B12 X=20 B/2 Y/2 X=30 P[Y= 1| X= 1] = 1- a a/2 7/2 O Y = 1 P[Y= 2 | X= 2] = 1-B Y = 2 OY=3 P[Y=3 | X=3] = 1- Y Figure P1.32 Ternary communication channel.