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> "Rare" is soon if you roll the dice fast enough.

Indeed. One fun example is LHC[1], where the probability of a proton in a single bunch hitting a proton in the bunch going the opposite direction is on the order of 10^-21, yet due to huge number of protons per bunch and large number of bunches per second, it still results in ~10^9 collisions per second.

[1]: https://www.lhc-closer.es/taking_a_closer_look_at_lhc/0.lhc_...



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