1)Possibility means that something might happen or be true and is used with "of" or "that" Ex.There is a possibility that I might go to London to study for 2 years. 2)Opportunity suggests it is possible for you to do something because the circumstances are good or lucky at the time Ex. I had the opportunity to spend 2 years in London while I was a student.

A 'possibility' is just one of several things that could be done, it is possible. 'He had the possibility either to stay in Paris or to spend the whole vacation in New York with his uncle." So both here are available options . 'Opportunity' is a chance to do something ,or a situation that facilitate doing something ,specially if it is something you already desired or wished before. "He always dreamt of working for this enterprise and just last week he got the opportunity to sit and talk with the chairman himself." However 'possibiliteS' as a plural noun has a meaning nearer to 'opportunity'. It means opportunities to develop in a successful, interesting, or exciting way " This old building has some intriguing possibilities."