  Let $\pi:\aut(F_n)\rightarrow \aut(\Z^n)$ be the epimorphism induced by the
isomorphism $\Z^n \cong F_n/F_n'$ and define $\mathcal{T}_n:=\ker\pi$. We prove
that the subset of $\mathcal{T}_n$ consists of all non-iwip and all
non-hyperbolic elements is exponentially small.
