"a slight push with the elbow," 1787, from nudge (v.). Figurative sense of "a signal or hint intended to call attention, remind, etc." is by 1831.
Old English beacen "sign, portent, lighthouse," from West Germanic *baukna "beacon, signal" (source also of Old Frisian baken, Old Saxon bokan, Old High German bouhhan); probably from Proto-Germanic *baukna- "beacon, signal," from suffixed form of PIE root *bha- (1) "to shine." Figurative use from c. 1600.
mid-15c., probabilite, "likelihood of being realized, appearance of truth, quality of being probable," from Old French probabilite (14c.) and directly from Latin probabilitatem (nominative probabilitas) "credibility, probability," from probabilis (see probable).
Meaning "something likely to be true" is from 1570s; mathematical sense is from 1718, "frequency with which a proposition similar to the one in question is found true in the course of experience."
In weather forecasting, probabilities was used in U.S. from 1869 and adopted in the official weather forecasts of the United States Signal Service; hence Old Probabilities, a humorous name for the chief signal officer of the Signal Service Bureau (by 1875).