In the present study, the sub-grid PDF of a progress variable approach has been investigated, in order to evaluate the capability of common sub-grid PDF models for the mixture fraction as well as a reactive progress variable. Hybrid LES/Monte-Carlo-transported PDF (MC-TPDF) simulations using a flamelet generated manifolds (FGM) progress variable approach have been performed of a non-premixed bluff-body stabilized CH4/H2 flame. Time averaged results of velocities, mixture fraction, temperature and OH mass fraction are shown and compared with presumed PDF results and experimental data. Furthermore, in order to assess the suitability of β-shaped PDF, especially for the reactive progress variable, instantaneous sub-grid distributions and third central moments of MC-TPDF and presumed β-PDF are compared. The obtained results show, that a presumed β-PDF is not a feasible model for the sub-grid PDF of the progress variable.