1
general::
Without order or fixed purpose, haphazardly, as in Jackson Pollock dropped paints on canvas seemingly at random. Originally this phrase meant "very speedily" and "heedlessly." Shakespeare had the present usage in I Henry VI (5:3): "He talks at random; sure the man is mad." [Late 1500s]
American Heritage Idioms
2
general::
Phrase(s): at random
by chance; haphazard. • The lottery numbers are chosen at random. • As a prank, the children dialed phone numbers at random.
McGrawhill's American Idioms And Phrasal Verbs