  In a recent paper (Cucker, Krick, Malajovich and Wschebor, A Numerical
Algorithm for Zero Counting. I: Complexity and accuracy, J. Compl.,24:582-605,
2008) we analyzed a numerical algorithm for computing the number of real zeros
of a polynomial system. The analysis relied on a condition number kappa(f) for
the input system f. In this paper, we look at kappa(f) as a random variable
derived from imposing a probability measure on the space of polynomial systems
and give bounds for both the tail P{kappa(f) > a} and the expected value E(log
kappa(f)).
