  We present a new measurement of the mass of the Milky Way (MW) based on
observed properties of its largest satellite galaxies, the Magellanic Clouds
(MCs), and an assumed prior of a {\Lambda}CDM universe. The large,
high-resolution Bolshoi cosmological simulation of this universe provides a
means to statistically sample the dynamical properties of bright satellite
galaxies in a large population of dark matter halos. The observed properties of
the MCs, including their circular velocity, distance from the center of the MW,
and velocity within the MW halo, are used to evaluate the likelihood that a
given halo would have each or all of these properties; the posterior PDF for
any property of the MW system can thus be constructed. This method provides a
constraint on the MW virial mass, 1.2 +0.7 -0.3(stat.) +0.3 -0.4 (sys.) x 10^12
M\odot (68% confidence), which is consistent with recent determinations that
involve very different assumptions. In addition, we calculate the posterior PDF
for the density profile of the MW and its satellite accretion history. Although
typical satellites of 10^12 M\odot halos are accreted over a wide range of
epochs over the last 10 Gyr, we find a \sim72% probability that the Magellanic
Clouds were accreted within the last Gyr, and a 50% probability that they were
accreted together.
