We investigated by deep-level transient spectroscopy a series of p-Si 1ϪX Ge X samples after in-diffusion of Zn. The measurements reveal two deep hole traps which are attributed to the Zn 0/Ϫ single-and Zn Ϫ/2Ϫ double-acceptor states of isolated Zn atoms on substitutional sites. The corresponding transient peaks are broadened for XϾ0 in comparison to those in pure silicon due to statistical fluctuations of the SiGe alloy composition in the local environment of the Zn atoms. This effect is described quantitatively within the alloy-broadening model which furthermore allows to determine the number of atoms sampled by the defect wave function. The results are compared with ab initio calculations for substitutional Zn in pure Si using the linear muffin-tin orbital method in the atomic-spheres approximation based on the local-density approximation. To model the Ge alloying, we have also studied trigonal pairs of substitutional Zn in Si with a single Ge ligand at different pair distances. From these results, the broadening of the transients can be understood qualitatively.