Chances are it is a 230/240V fan.
If it wasn't there would be a transformer somewhere.
Nobody has any idea if there is, or is not.
As the old fan has now been thrown away, and all that's left is a cable coming out of the wall, how can you say that there isn't a transformer somewhere?
I am not saying that at all. (Read the quote again.) I am saying if the fan wasn't 230/240V (and therefore 12V typically) then I would expect there to be a 12V transformer somewhere.
See what I mean?
No - you did not say "if... then...", you said "chances are...", i.e. you were asserting that it is more likely than not that is is a 230/240V fan.
I'll rephrase my question.
How can you say that there is a less than 0.5 probability (or less than 0.x, whatever you regard as the threshold for 1-0.x to be "chances are") that there is no transformer just because one has not been found, given that no search for one has been undertaken?