Probability (p(j ∈ k|d_j, {β}) in Eq. (23)) of each mock observation to belong to the Pop. III class in the left to right columns as a function of primary mass (m_1, d), secondary mass (m_2, d), and luminosity distance (d_L). Each dot corresponds to the median of the posterior samples. The top, middle, and bottom rows correspond to the fiducial, optimistic, and pessimistic scenarios, respectively. The red (blue) dots indicate observations known to belong to Pop. I–II (Pop. III). We refer to Sect. 2.4 for details.