Problem 27 Consider a communication system. At any given time, the communication channel is in good condition with probability 0.8, and is in bad condition with probability 0.2. An error occurs in a transmission with probability 0.1 if the channel is in good condition, and with probability 0.3 if the channel is in bad condition. Let G be the event that the channel is in good condition and E be the event that there is an error in transmission. a. Complete the following tree diagram: 1 P(E|G) P(GE) P(G) P(G) P(ECG) P(GEC) P(GC) b. Using the tree find P(E). c. Using the tree find P(G|E). P(E|GC) P(Gn E) P(GC) P(ECGC) P(GC EC)