Decision makers of companies often face the dilemma of whether to
 release data for knowledge discovery, vis a vis the risk of disclosing
 proprietary or sensitive information. While there are various ``sanitization''
 methods, in this paper we focus on anonymization, given its widespread
 use in practice. We give due diligence to the question of ``just how
 safe the anonymized data is'', in terms of protecting the true
 identities of the data objects. We consider both the scenarios when
 the hacker has no information, and more realistically, when the
 hacker may have partial information about items in the domain. 
 We conduct our analyses in the context of frequent set
 mining.  We propose to
 capture the prior knowledge of the hacker by means of a \emph{belief
 function}, where an educated guess of the frequency of each item is
 assumed. For various classes of belief functions, which correspond
 to different degrees of prior knowledge, we derive formulas for
 computing the expected number of ``cracks''. While obtaining the exact values
 for the more general situations is computationally hard,
 we propose a heuristic called the \emph{O-estimate}.
 It is easy to compute, and is shown to be accurate empirically
 with real benchmark datasets. Finally, based on the O-estimates, we
 propose a recipe for the decision makers to resolve their dilemma.