The grand canonical ensemble Monte Carlo simulations have been carried out to investigate the thermodynamic and structural properties of hard-sphere fluids confined within a spherical hard-wall pore. Equilibrium partition coefficients and pore density profiles are computed over a wide range of particle-to-pore size ratios and concentrations distributing between an external bulk phase and a pore phase. The simulation data for equilibrium partitioning are used to assess the limitations and applicabilities of theoretical approximations including the virial expansion equation and the extended two-state prediction. The Monte Carlo results obtained in these studies, in conjunction with the theoretical models, provide the basis for a discussion on the steric effects in size-exclusion partitioning of such systems.