“Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the die will come up proximately 1 ,000,000,000 times) and the improbable (that in six throws with the same die the one will come approximately up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable.
But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term "probability" includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification.

Cf. Ernst Mally's Probability and Law, Hans Reichenbach The theory Probability, Whitehead and Russell's Principia Mathematica, von Mises' Probability, Statistics and Truth”