Well, yes. But the point is that random sampling lets you do it without thinking. Even better, it can sample over multiple spaces at the same time, and over spaces we haven't even yet formalized. "Civilization advances by extending the number of important operations which we can perform without thinking of them." (Whitehead)

An example is something like "pairwise testing" of arguments to a function. Just randomly generating values will hit all possible pairs of values to arguments, again with a logarithmic penalty.