  If a small fraction of Fast Radio Bursts (FRBs) are associated with Gamma-Ray
Bursts (GRBs), as recently suggested by Zhang, the combination of redshift
measurements of GRBs and dispersion measure (DM) measurements of FRBs opens a
new window to study cosmology. At $z<2$ where the universe is essentially fully
ionized, detections of FRB/GRB pairs can give an independent measurement of the
intergalactic medium portion of the baryon mass fraction, $\Omega_b f_{\rm
IGM}$, of the universe. If a good sample of FRB/GRB associations are discovered
at higher redshifts, the free electron column density history can be mapped,
which can be used to probe the reionization history of both hydrogen and helium
in the universe. We apply our formulation to GRBs 101011A and 100704A that each
might have an associated FRB, and constrained $\Omega_b f_{\rm IGM}$ to be
consistent with the value derived from other methods. The methodology developed
here is also applicable, if the redshifts of FRBs not associated with GRBs can
be measured by other means.

High Energy Astrophysical Phenomena