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The question is to compute or estimate the following probabilty.

Suppose that you have $N$ (e.g. 30) tasks, each of which repeats every $t$ min (e.g. 30 min) and lasts $l$ min (e.g. 5 min). If the tasks started at uniformly random point in time yesterday, what is the probability that there is a time today at which at least $m$ (e.g. 10) of the tasks run.

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