A new air-shower core-detector array (YAC: Yangbajing Air-shower Core-detector array) has been developed to measure the primary cosmic-ray composition at the "knee" energies in Tibet, China, focusing mainly on the light components. The YAC-II consisting of 124 detectors has been constructed and operated at Yangbajing (4300 m a.s.l.) in Tibet since February 2014. The YAC-II has been placed near the center of the Tibet-III AS array and operates together with Tibet-III and a large underground water-Cherenkov muon-detector array (MD). In this paper, we have performed a detailed Monte Carlo simulation to check the sensitivity of YAC-II+Tibet-III+MD array to the light components in the primary cosmic rays around the knee energies, taking account of the observation conditions of actual YAC-II+Tibet-III+MD array. We have checked the sensitivity of YAC to the hadronic interaction models (QGSJET01c and SIBYLL2.1) and primary cosmic-ray composition models ("He-poor", "He-rich" and "Gaisser-fit") around the knee using the high-energy core events observed by the YAC-II+Tibet-III+MD array, and the capability of the measurement of the light-chemical components (proton, helium) with the new Tibet hybrid experiment is investigated. The simulation shows that the light-component spectrum estimated by our methods can well reproduce the input ones within 10% error, and there will be about 30% systematic errors mostly induced by the primary and interaction models used.