by mistake vs fortuitously

by mistake

prep
  • by accident; without intention to do so 

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