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4. [Communication network 1] Consider the communication network shown in the figure below and suppose that each link can fail with probability p. Assume

4. [Communication network 1] 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 statistically independant. (a) Find the probability that there exists a path from A to B. (b) Find the probability that there exists a path from A to B, given that exactly one link has failed. A Q 2 3 D B

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