by accident vs fortuitously

by accident

adv
  • Accidentally; unintentionally; without meaning to; as the result of an event not expected, aided, or willingly planned. 

  • As the result of some undesigned, unintended, unrelated, natural, or random occurrence; as the unexpected and unforeseen result of formerly unrelated factors. 

  • By chance; unexpectedly; as the result of an unrelated series of events. 

adj
  • Accidental; as the result of some unforeseen happening or series of events; unexpected; resulting from an event without the foresight, expectation, aid, or design of the person by whose agency it was caused; unintentional. 

fortuitously

adv
  • In a fortuitous manner; in a manner of happening by chance; coincidentally; accidentally. 

  • In a fortuitous manner; in a manner of happening by a lucky chance; luckily; fortunately. 

How often have the words by accident and fortuitously occurred in a corpus of books? (source: Google Ngram Viewer )