  The LIGO Scientific and Virgo Collaborations have announced the first
detection of gravitational waves from the coalescence of two neutron stars. The
merger rate of binary neutron stars estimated from this event suggests that
distant, unresolvable binary neutron stars create a significant astrophysical
stochastic gravitational-wave background. The binary neutron star background
will add to the background from binary black holes, increasing the amplitude of
the total astrophysical background relative to previous expectations. In the
Advanced LIGO-Virgo frequency band most sensitive to stochastic backgrounds
(near 25 Hz), we predict a total astrophysical background with amplitude
$\Omega_{\rm GW} (f=25 \text{Hz}) = 1.8_{-1.3}^{+2.7} \times 10^{-9}$ with
$90\%$ confidence, compared with $\Omega_{\rm GW} (f=25 \text{Hz}) =
1.1_{-0.7}^{+1.2} \times 10^{-9}$ from binary black holes alone. Assuming the
most probable rate for compact binary mergers, we find that the total
background may be detectable with a signal-to-noise-ratio of 3 after 40 months
of total observation time, based on the expected timeline for Advanced LIGO and
Virgo to reach their design sensitivity.
