Suppose we have $N$ identical machines, at any given hour, there's a chance $P$ that any given machine went down. A down machine takes $T$ hours to recover. How do I calculate the chances that in a given longer interval $Y$ (assume $Y >> T$), what are the probability that there exists hour $t$, $0 < t < Y$, such that at $t$ there are more than $R$ machines that are down?
2026-04-12 20:53:54.1776027234
Probability of more than n machines down any hour?
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