1650s, "having no definite aim or purpose, haphazard, not sent in a special direction," from phrase at random (1560s), "at great speed" (thus, "carelessly, haphazardly"), from an alteration of the Middle English noun randon, randoun "impetuosity; speed" (c. 1300). This is 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.)). For spelling shift of -n to -m, compare seldom, ransom.
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 that need not be read sequentially is recorded from 1953. Related: Randomly; randomness.