for all I know vs possibly

for all I know

possibly

adv
  • In the realm of possibility; indicates that the action may successfully be performed (is not impossible) regardless of any facts or circumstances known to, stated by or implied by the speaker that might limit the performance. 

  • Perhaps; indicates that the proposition may be true (is not certainly false) regardless of any facts or circumstances known to, stated by or implied by the speaker. 

How often have the words for all I know and possibly occurred in a corpus of books? (source: Google Ngram Viewer )