The phrase "a big possibility of" is correct and usable in written English.
It can be used when discussing the likelihood or chance of something occurring.
Example: "There is a big possibility of rain tomorrow, so we should bring our umbrellas."
Alternatives: "a strong chance of" or "a high likelihood of".
"There is a big possibility of … President [Lula] being a candidate again either in 2014 or in 2018," admitted Marcia Carvalho Lopes, Brazil's minister for social development.
"If he [Clattenburg] doesn't think twice, it's a penalty and a red card with a big possibility of 2-2 and a lot of time to go.
I'm aware that there's a big possibility of being on the practice squad for however long they see fit". What he can be sure of, at least, is that he has already made an impression on his new employers.
"We knew if we came to half-time still 0-0 or not conceding we would have a big possibility of taking something away from here.
Nevertheless, there is a bigger possibility of an error occurrence when a greater number of parameters is being estimated.
On Thursday, Ms. de Lima said that "there is a big possibility" that some of the hostages may have been hit by "friendly fire".
Last week, Ms. de Lima had said there was "a big possibility" that some of the hostages could have been hit by "friendly fire," noting that ballistic experts indicated that the hostage-taker could not have killed all the victims.
"It gives a big possibility," he said, "but of course we don't know".
If the PRC steps in, then it is a big possibility," said Carlos Fernando Chamorro, editor of the Confidencial newspaper.
"There is a big possibility that you are part of the problem without even knowing it," said Paul Vixie, chairman of the Internet Software Consortium, a nonprofit company responsible for the software used by many of the servers that power the Internet.
