Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume that failures of different links are independent.

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Consider the communication network shown in the figure below and suppose that each
link can fail with probability p. Assume that failures of different links are independent.
Link 1
A
Link 3
Link 2
Link 4
Link 5
B
(a) Assume that p = 1/3. Find the probability that there exists a path from A to B
along which no link has failed.
(b) Given that exactly one link in the network has failed, find the probability that there
exists a path from A to B along which no link has failed
Transcribed Image Text:Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume that failures of different links are independent. Link 1 A Link 3 Link 2 Link 4 Link 5 B (a) Assume that p = 1/3. Find the probability that there exists a path from A to B along which no link has failed. (b) Given that exactly one link in the network has failed, find the probability that there exists a path from A to B along which no link has failed
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