The phrase "a much higher possibility" is correct and usable in written English.
It can be used when discussing the likelihood or chance of something occurring, especially in a comparative context.
Example: "Given the new evidence, there is now a much higher possibility that the theory is correct."
Alternatives: "a significantly greater chance" or "a far more likely scenario."
In actual fact they've levelled off to unacceptable rates and most of those kids who are overweight or obese have a much higher possibility of suffering a wide range of diseases.
"While of course there is a risk of mischief, I think there is a much higher possibility of transforming the usefulness of this data on a much more positive set of agendas.
Deloitte, too, is one of a number of employers - others include the BBC, HSBC and the National Health Service - singled out by Prime Minister David Cameron for partaking in a "name-blind" recruitment initiative after it emerged that people with white-sounding names ended up with a much higher possibility of being shortlisted for a job.
Compared with those living in the countryside, couples living in cities have a much higher possibility of divorce.
Patients with an NRILN have a much higher possibility of iatrogenic vocal cord paralysis due to intraoperative injury of the recurrent nerve [18].
Whereas high safety measures are normally standard at production sites, especially in the chemical industry, the handling of ENM in manufacturing of the final products is much less controlled and can result in a much higher possibility for release [7, 72, 73].
That opens up the possibility of a much higher density data storage devices.
"If I have to pay, I have to pay," Mr. Suss said about the possibility of a much higher fare.
The people said that the senator wanted to spare his companion the rigors of a high-profile trial and the possibility of a much higher sentence, but that the decision was a complex one and that he chose to plead for other reasons as well.
It has the possibility of a much higher energy yield per unit, so it can be much more efficient.
An alternative semantics of the word 'know' will de-emphasize the importance of the salience or non-salience of error possibilities, and ascribe a much higher degree of semantic independence to the subjects who use the word 'know'know
