Corresponding character matching probability

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SUMMARY

The discussion focuses on calculating the probability of matching k-mers in a protein dataset consisting of 10,000 sequences. Specifically, it addresses the probability that a k-mer "b" from one sequence matches a k-mer "a" from another sequence in at least r positions out of k total positions. The probability is determined by the frequency of amino acids in the dataset, emphasizing that without numerical data, an exact probability cannot be established. This highlights the importance of statistical analysis in bioinformatics for sequence comparison.

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I have a dataset of protein, consisting of 10000 sequence each, having length Si
, where 1<=i<=10000. Now, I extracted k-mer "a" from the 1st sequence. The probability of occurrence of amino acid (character of protein sequence) is given by its frequency in the dataset. If I choose k-mer "b" from other sequence, what will be the probability that k-mer "b" matches k-mer "a" at least in r position out of k position?
 
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I believe that would be the probability that k-mer a appears in the remaining 9999 sequences. Without numerical data we can't give an exact value.
 

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