why are the orbitals of the hydrogen atom described as probability maps? Why are the edges of the hydrogen orbitals sometimes drawn to appear "fuzzy"?

Answer 1

Truth be known, they are drawn to be fuzzy because we really don't know EXACTLY where they are. It is best if we describe the probability of an electron being within that range. In fact, the whole idea of orbits and sub-orbits (orbitals) is a carry over from the old days of Bohr, Sommerfeld, Rydberg, Balmer, etc. Wave mechanics comes the closest we have today to describing an atom and students (and many professors) simply don't have the math background to engage in a discussion using wave mechanics. So we rely on the picture method instead.