Find out the probability of a path break for an eight-hop path given that the probability of a link break is p?

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Can we apply Binomial distribution here? How do I approach it? How the method will change when topology change from linear to ring topology?

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I'm assuming that link breaks are independent random events, but you should state all such specifications in the question. For both, find the probability that it doesn't break. For the ring topology, the answer would depend on what you mean by "a path break" and "an eight-hop path", but the method should be the same.