The existence of pentaquarks, namely, baryonic states made up of four quarks and one antiquark, became questionable, because the candidates, i.e. the Θ+ peak, are seen in certain reactions, i.e. p+p collisions, but not in others, i.e. e+e− annihilations. In this paper, we estimate the production of Θ+(1540) and Ξ--(1860) in e+e− annihilations at different energies using the Fermi statistical model as originally proposed in its microcanonical form. The results are compared with that from proton-proton (pp) collisions at SPS (CERN’s superco...