The apparent dependence of detection frequency of extrasolar planets on the metallicity of their host stars is investigated with Monte Carlo simulations using a deterministic core-accretion planet formation model. According to this model, gas giants formed and acquired their mass M_p through planetesimal coagulation followed by the emergence of cores onto which gas is accreted. These protoplanets migrate and attain their asymptotic semimajor axis a through tidal interaction with their nascent disk. Based on the observed properties of protostellar disks, we generate an M_p-a distribution. Our results reproduce the observed lack of planets with intermediate mass M_p = 10-100 M_⊕ and a 3 AU and with large mass M_p 10³ M_⊕ and a 0.2 AU. Based on the simulated M_p-a distributions, we also evaluate the metallicity dependence of the fraction of stars harboring planets that are detectable with current radial velocity surveys. If protostellar disks attain the same fraction of heavy elements as contained in their host stars, the detection probability around metal-rich stars would be greatly enhanced because protoplanetary cores formed in them can grow to several Earth masses prior to their depletion. These large masses are required for the cores to initiate rapid gas accretion and to transform into giant planets. The theoretically extrapolated metallicity dependence is consistent with the observations. This correlation does not arise naturally in the gravitational-instability scenario. We also suggest other metallicity dependences of the planet distributions that can be tested by ongoing observations.