The Word is Random

OTHER WORD CHOICES:  chance, accidental, haphazard, unsystematic, hit and miss

AND yes, arbitrary is another word for Random.

Here are two off the wall words that I found that also can be synonyms for Random:

Stochastic:  (stuh-KAS-tik) adjective: Involving chance; random; probabilistic.
     Etymology:  From Greek stokhos (aim, target, a pointed stake for an archer to aim at). Earliest documented use: 1662.
     Usage:  “Medicine is a stochastic science — no doctor can predict the future.”  Sandeep Jauhar; When Doctors Slam the Door; The New York Times; Mar 16, 2003.