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We present a model for the probability of random sequences appearing in product ion spectra obtained from tandem mass spectrometry experiments using collision-induced dissociation. We demonstrate the use of these probabilities for ranking candidate peptide sequences obtained using a de novo algorithm. Sequence candidates are obtained from a spectrum graph that is greatly reduced in size from those in previous graph-theoretical de novo approaches. Evidence of multiple instances of subsequences of each candidate, due to different fragment ion type series as well as isotopic peaks, is incorporated in a hierarchical scoring scheme. This approach is shown to be useful for confirming results from database search and as a first step towards a statistically rigorous de novo algorithm.