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: P(E|G) P(Gn E) P(G) P(G) P(E©|G) P(G n EC) 1 P(G) P(EIG) P(G n E) P(G°) P(E IG P(G n EC) b. Using the tree find P(E). c. Using the tree find P(G|E°).

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