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°).
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°).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
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Transcribed Image Text:Problem-4
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(EC|G)
P(GN EC)
P(GC)
P(E|GC)
P(G n E)
P(GC)
P(E°|G©
P(G n EC)
b. Using the tree find P(E).
c. Using the tree find P(G|E).
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