A statistical impossibility is a probability that is so low as to not be worthy of mentioning. Sometimes it is quoted as 10-50[1] although the cutoff is inherently arbitrary. Although not truly impossible the probability is low enough so as to not bear mention in a rational, reasonable argument.
In some cases that arise in Gedanken experiments in thermodynamics, the probabilities can be approximately 10Avogadro's number, that is, 101023, give or take a few billion orders of magnitude.