"having no definite aim or purpose," 1650s, from at random (1560s), "at great speed" (thus, "carelessly, haphazardly"), alteration of Middle English randon "impetuosity, speed" (c.1300), from Old French randon "rush, disorder, force, impetuosity," from randir "to run fast," from Frankish *rant "a running," from Proto-Germanic *randa (cf. Old High German rennen "to run," Old English rinnan "to flow, to run;" see run (v.)).
In 1980s 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.