Background: It has become increasingly apparent that the trophectoderm (TE) at blastocyst stage is much more mosaic than has been appreciated. Whether preimplantation genetic screening (PGS), utilizing a single TE biopsy (TEB), can reliably determine embryo ploidy has, therefore, increasingly been questioned in parallel. Methods: We for that reason here established 2 mathematical models to assess probabilities of false-negative and false-positive results of an on average 6-cell biopsy from an approximately 300-cell TE. This study was a collaborative effort between investigators at The Center for Human Reproduction in New York City and the Center for Studies in Physics and Biology and the Brivanlou Laboratory of Stem Cell Biology and Molecular Embryology, the latter two both at Rockefeller University in New York City. Results: Both models revealed that even under best case scenario, assuming even distribution of mosaicism in TE (since mosaicism is usually clonal, a highly unlikely scenario), a biopsy of at least 27 TE cells would be required to reach minimal diagnostic predictability from a single TEB. Conclusions: As currently performed, a single TEB is, therefore, mathematically incapable of reliably determining whether an embryo can be transferred or should be discarded. Since a single TEB, as currently performed, apparently is not representative of the complete TE, this study, thus, raises additional concern about the clinical utilization of PGS.