My understanding of circuits which are not supplied an e.m.f. is that the electrons randomly just flow about in random directions, and since there's so many of them, probability dictates that any forwards or useful movement is cancelled almost perfectly by the negative or unwanted movement.
If this understanding is correct, is it theoretically possible for the electrons to, under an extremely low probability, mostly flow in the correct direction, and generate a current, perhaps lighting up a lamp? I'm talking even probabilities like 1x10^-1000, just wondering if it is at all possible.
This seems wrong to me and if anyone could explain why this is not possible, or the flaw in my logic, that would be greatly appreciated.
Apologies if there's some huge hole in my logic, or I'm being extremely stupid, I'm a student studying Physics below university level and thus know little more than basic outlines of Physical theories.