Successful Probability of a Communication Network Diagram
Problem 742
Consider the network diagram in the figure. The diagram consists of five links and each of them fails to communicate with probability $p$. Answer the following questions about this network.
(1) Determine the probability that there exists at least one path from A to B where every link on the path functions without errors. Express the answer in term of $p$.
(2) Assume that exactly one link has failed. In this case, what is the probability that there is a successful path from A to B, that is, each link on the path has not fail.
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