We perform the first simultaneous extraction of unpolarized parton distributions and fragmentation functions from a Monte Carlo analysis of inclusive and semi-inclusive deep-inelastic scattering, Drell-Yan lepton-pair production, and single-inclusive e + e − annihilation data. We use data resampling techniques to thoroughly explore the Bayesian posterior distribution of the extracted functions, and use k-means clustering on the parameter samples to identify the configurations that give the best description across all reactions. Inclusion of the semi-inclusive data reveals a strong suppression of the strange quark distribution at parton momentum fractions x 0.01, in contrast with the ATLAS observation of enhanced strangeness in W ± and Z production at the LHC. Our study reveals significant correlations between the strange quark density and the strange → kaon fragmentation function needed to simultaneously describe semi-inclusive K ± production data from COMPASS and inclusive K ± spectra in e + e − annihilation from ALEPH and SLD, as well as between the strange and light antiquark densities in the proton.