Question: Consider a c ommunication system. At any given time, the communication channel is in good condition with probability 0.8, and is in bad condition with

Consider a c ommunication 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(G) P(GC) P(G) P(E|G) P(ECG) P(E|GC) P (G) P(ECGC) P(Gn E) P(Gn EC) P(GenE) P(GC NEC)

b. Using the tree find P(E).

c. Using the tree find P(G|E^c).

1 P(G) P(GC) P(G) P(E|G) P(ECG) P(E|GC) P (G) P(ECGC) P(Gn E) P(Gn EC) P(Gen E) P(GenEC)

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