$\newcommand{\bra}[1]{\left<#1\right|}\newcommand{\ket}[1]{\left|#1\right>}\newcommand{\bk}[2]{\left<#1\middle|#2\right>}\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}$Given a mixed state $\rho = \sum p_k \rho_k$ that is an statistical emsemble, where each "state" $\rho_k$ on the upper half of the Bloch sphere
appears with equal probability. The states don't lie on the surface of the Bloch sphere but at a radius of $1/{2\pi}$, such that the sum, which, in the continous case turns out to be an integral, properly works out. So the $\rho_k$ are not pure states!
If I now measure the system in the computational basis, I'll get $\ket0$ in 100% of the cases. So I would assume the state is a pure one, but is it?
We might need infinitely many states $\rho_k$, but maybe a big number is enough to get a good aprroximation. Or did I miss something else?