"possibility for someone" is a correct and usable phrase in written English.
You can use it when describing a potential opportunity or outcome that someone has. For example, you could say, "The internship provides a great possibility for someone interested in engineering."
He said he had not been in that situation, "but you probably don't see the opportunity as much as the possibility for someone to catch you".
Some experts predicted the San Francisco 49ers might take Rodgers, who played at California, as the No. 1 pick, a thrilling possibility for someone who grew up idolizing Joe Montana.
The problem is that without any one individual in charge in Europe, there is virtually no possibility for someone to emerge the way that Mr. Paulson did during the panic of 2008 with a lifeline like the Troubled Asset Relief Program, a plan he practically had to ram down the throat of Congress.
"And there's always a middle ground possibility for someone to say, 'I'm for commonsense gun laws.
"There's always a middle ground possibility for someone to say, 'I'm for common sense gun laws.
I worried what would happen if I suddenly had to move to another city for work, a very real possibility for someone starting out in newspapers.
There are a number of possibilities for someone with his business acumen.
Listed below are career possibilities for someone with a MLS degree: Researcher.
[So] there is little possibility of someone examining people's purchasing habits or for that information to be used against the purchaser in the future.
While a planned overhaul would give publishers a bit more protection, the rise of social media like Twitter has vastly expanded the possibilities for libeling someone.
"There's always a possibility of someone counterbidding".
