The phrase "a possibility which" is correct and usable in written English.
It can be used when discussing potential outcomes or scenarios that may occur in a given context.
Example: "There is a possibility which could lead to significant changes in our approach to the project."
Alternatives: "an option that" or "a chance that".
It is a possibility which President Hoover can hardly ignore.
Anonymity becomes a possibility, which lessens the fear of stigma.
That is a possibility which the new austerity plan has not yet entirely banished.
He said nothing about teaming up with Kroenke to mount a takeover bid proper, a possibility which would probably dismay the current board.
He hinted at a possibility, which he has raised in the past, that he would call Judge Stearns and Mr. Mueller as witnesses.
Peter Smithson, who has died aged 79, was a Durham lad who, as a young man, made no secret of his intention to become "the world's greatest architect", a possibility which his peers tended to accept.
But other EU leaders must now accept that a UK referendum is a reality, not a vague possibility, which changes the rules of engagement.
In the end, the last empire may prove to be an empire of nothing at all ― a grim possibility which has been a focus of TomDispatch, the website I've run since November 2002.
A promising possibility, which is still at a very early stage, is supercooled ionic liquid crystals for fast ion diffusion through the guided channels of a liquid-like medium.
While the northern origin theory has been dismissed by many historians, the epigraphist K. V. Ramesh has suggested that an earlier southern migration is a distinct possibility which needs examination.
A fourth possibility, which scientists consider unlikely, is bioterrorism: a new virus might have been genetically engineered in a laboratory, and might then have escaped or been released on purpose.
