Summary: The 2D (two-dimensional) contingency tables have been used in many aspects of our daily life. In practice, errors may be incurred when generating or editing such a table hence the data contained by the table could be inaccurate. Even so, it is still possible for a knowledgeable snooper who may have acquired the information of error distributions to decipher some private information from a released table. This paper investigates the estimation of privacy disclosure probability for contingency tables with inaccurate data based on Fréchet bounds and proposes two optimization solutions for the control of privacy disclosure so as to preserve private information. Our estimation of privacy disclosure probability and the optimization solutions are also applicable to error-free tables which can be regarded as a special case where there are no errors. The effectiveness of the solutions is verified by rigorous experiments.