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This correspondence is concerned with probabilistic fault diagnosis for digital systems. A graph-theoretic model of a diagnosable system introduced by Preparata et al. is considered in which a system is made up of a number of units with the probability of failure. The necessary and sufficient conditions are obtained for the existence of testing links (a connection) to form probabilistically t-diagnosable systems with and without repair. Methods for connection assignments are given for probabilistic fault diagnosis procedures with and without repair. Maheshwari and Hakimi  gave the necessary and sufficient condition for a system to be probabilistically t-diagnosable Without repair. In this correspondence, we show the necessary and sufficient condition for a system to be probabilistically t-diagnosable with repair.