  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 $M_{\rm p}$ through
planetesimal coagulation followed by the emergence of cores onto which gas is
accreted. These protoplanets migrate and attain their asymptotic semi-major
axis $a$ through their tidal interaction with their nascent disk. Based on the
observed properties of protostellar disks, we generate $M_{\rm p}$-$a$
distribution. Our results reproduce the observed lack of planets with
intermediate mass $M_{\rm p} = 10$--100$M_{\oplus}$ and $a \la 3$AU and with
large mass $M_{\rm p} \ga 10^3 M_{\oplus}$ and $a \la 0.2$AU. Based on the
simulated $M_{\rm p}$-$a$ distributions, we also evaluate the metallicity
dependence of fraction of stars harboring planets that are detectable with
current radial velocity survey. If protostellar disks attain the same fraction
of heavy elements which are 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 observation. This
correlation does not arise naturally in the gravitational-instability scenario.
We also suggest other metallicity dependence of the planet distributions that
can be tested by on-going observations.
