  In the literature, compact binary coalescences (CBCs) have been proposed as
one of the main scenarios to explain the origin of some non-repeating fast
radio bursts (FRBs). The large discrepancy between the FRB and CBC event rate
densities suggest their associations, if any, should only apply at most for a
small fraction of FRBs. Through a Bayesian estimation method, we show how a
statistical analysis of the coincident associations of FRBs with CBC
gravitational wave (GW) events may test the hypothesis of these associations.
We show that during the operation period of advanced LIGO, the detection of
$\sim100$ ($\sim1000$) GW-less FRBs with dispersion measure (DM) values smaller
than 500 ${\rm pc~cm^{-3}}$ could reach the constraint that less than $10\%$
(or $1\%$) FRBs are related to binary black hole (BBH) mergers. The same number
of FRBs with DM values smaller than 100 ${\rm pc~cm^{-3}}$ is required to reach
the same constraint for binary neutron star (BNS) mergers. With the upgrade of
GW detectors, the same constraints for BBH and BNS mergers can be reached with
less FRBs or looser requirements for the DM values. It is also possible to pose
constraints on the fraction of each type of CBCs that are able to produce
observable FRBs based on the event density of FRBs and CBCs. This would further
constrain the dimensionless charge of black holes in binary BH systems.
