"having no definite aim or purpose," 1650s, from at random (1560s), "at great speed" (thus, "carelessly, haphazardly"), alteration of Middle English noun randon "impetuosity, speed" (c. 1300), from Old French randon "rush, disorder, force, impetuosity," from randir "to run fast," from Frankish *rant "a running" or some other Germanic source, from Proto-Germanic *randa (source also of Old High German rennen "to run," Old English rinnan "to flow, to run;" see run (v.)).
In 1980s U.S. college student slang it began to acquire a sense of "inferior, undesirable." (A 1980 William Safire column describes it as a college slang noun meaning "person who does not belong on our dormitory floor.") Random access in reference to computer memory is recorded from 1953. Related: Randomly; randomness.