A bound on the expected number of random elements to generate a finite   group all of whose Sylow subgroups are d-generated
  Assume that all the Sylow subgroups of a finite group $G$ can be generated by $d$ elements. Then the expected number of elements of $G$ which have to be drawn at random, with replacement, before a set of generators is found, is at most $d+\eta$ with $\eta \sim 2.875065.$ 
Andrea Lucchini
math.GR