  Globular clusters (GCs) effectively produce dynamically-formed low-mass X-ray
binaries (LMXBs). Observers detect ~100 times more LMXBs per stellar mass in
GCs compared to stars in the fields of galaxies. It has also been
observationally established that metal-rich GCs are about 3 times more likely
to contain an X-ray source than their metal-poor counterparts. Recent
observations have shown that this ratio holds in extragalactic GCs for all
bright X-ray sources with Lx between 2X10^{37} and 5X10^{38} erg/s. In this
Letter, we propose that the observed metallicity dependence of LMXBs in
extragalactic GCs can be explained by the differences in the number densities
and average masses of red giants in populations of different metallicities. Red
giants serve as seeds for the dynamical production of bright LMXBs via two
channels - binary exchanges and physical collisions - and the increase of the
number densities and masses of red giants boost LMXB production, leading to the
observed difference. We also discuss a possible effect of the age difference in
stellar populations of different metallicities.
