  This paper deals with the homogenization of the Poisson equation in a bounded
domain of $\mathbb{R}^d$, $d>2$, which is perforated by a random number of
small spherical holes with random radii and positions. We show that for a class
of stationary short-range correlated measures for the centres and radii of the
holes, we recover in the homogenized limit an averaged analogue of the "strange
term" obtained by Cioranescu and Murat in the periodic case [D. Cioranescu and
F. Murat, \textit{Un term \'etrange venu d'ailleurs} (1986)]. We stress that we
only require that the random radii have finite $(d-2)$-moment, which is the
minimal assumption in order to ensure that the average of the capacity of the
balls is finite. Under this assumption, there are holes which overlap with
probability one. However, we show that homogenization occurs and that the
clustering holes do not have any effect in the resulting homogenized equation.
