  The percolation threshold for flow or conduction through voids surrounding
randomly placed spheres is rigorously calculated. With large scale Monte Carlo
simulations, we give a rigorous continuum treatment to the geometry of the
impenetrable spheres and the spaces between them. To properly exploit finite
size scaling, we examine multiple systems of differing sizes, with suitable
averaging over disorder, and extrapolate to the thermodynamic limit. An order
parameter based on the statistical sampling of stochastically driven dynamical
excursions and amenable to finite size scaling analysis is defined, calculated
for various system sizes, and used to determine the critical volume fraction
phi_{c} = 0.0317 +/- 0.0004 and the correlation length exponent nu = 0.92 +/-
0.05.
