Without pattern that can be predicted. Randomness is a statement about knowledge as much as about the thing.
Old French randon (rush, great speed, disorderly haste), from randir (to run fast), of Germanic origin; random meant at great speed before it meant without a predictable pattern, the two senses joined by the idea of motion no one is steering.
Without pattern that can be predicted. The root's runaway speed is a fair image: randomness is a statement about what cannot be steered, as much as about what cannot be known in advance.