by coincidence vs fortuitously

by coincidence

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 coincidence and fortuitously occurred in a corpus of books? (source: Google Ngram Viewer )