fortuitously

unintentionally unwittingly

by mistake haphazardly

accidentally as luck would have it by a fluke by coincidence by mistake for some reason out of the clear blue sky unexpectedly unintentionally unwittingly

casually remotely

accidentally

as a by-product as side effect by the bye by the way in passing in related manner not by design obiter parenthetically subordinately unexpectedly

purposely

fortunately

by chance favorably opportunely propitiously providentially

unhappily unluckily

profitably strongly well

auspiciously flourishingly fortunately opportunely propitiously prosperously swimmingly thrivingly triumphantly victoriously

accidentally

circumstantially

by coincidence

advisedly deliberately intentionally normally obviously predictably regularly