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The phrase 'the possibility of whether' is not correct in written English.
Instead, you would use the phrase 'the possibility of whether/if'. For example, you could say, "We discussed the possibility of whether/if we should go on vacation this year."
Exact(28)
The Treasury has said Osborne currently has "no plans" to do so, as if it were discussing the possibility of whether he might go to the cinema.
Mr Hasan told GMTV that detectives were looking at the possibility of whether the kidnap was "a sort of inside job".
But before the day was out, investigators began to explore the possibility of whether it could have been an inside job, the authorities said.
What does each item do? 3. Explain to students that they are going to be acting as teams of NASA scientists exploring the possibility of whether or not human life could be sustained on other planets in our solar system.
-- We also suggest exploring the possibility of whether governments whose citizens have borne the bloody results of Bout's activities over the years, such as Sierra Leone, Liberia and Congo, would be willing to publicly express dismay/engage the Thai government on the verdict and whether any affected government would be willing to ask for his extradition.
We next investigated the possibility of whether Hcy-induced mitochondrial metabolic changes and T-cell activation are related to ER stress.
Similar(32)
"The meteorite may well help us get a better understanding of the possibilities of whether life existed on Mars in the past.
This may distinguish between the possibilities of whether H302A is initially phosphorylated on the mitochondria but cannot be retained over time and whether there is no Parkin Ubl Ser phosphorylation at all on mitochondria due to its inability to bind ubiquitinPhospho-Ser65 in the first instance.
Fourth, whereas all estimates of F are genome-wide estimates of autozygosity, genomic estimates of F can be altered to allow for the possibility of testing whether an effect of F is distributed evenly across the genome or whether the signal comes from specific genomic locations (e.g., by obtaining separate F estimates for different chromosomes).
"The possibility of surveillance, whether direct or through access to records of speech, research and exploration, undermines a democratic society," it continues.
I have noticed older single people avoiding new close friendships, to protect themselves from the possibility of hurt, whether from hoping for too much, or giving too little.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com