MHB Corresponding character matching probability

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The discussion focuses on calculating the probability of matching k-mers in a protein dataset of 10,000 sequences. It highlights that the probability of an amino acid's occurrence is based on its frequency within the dataset. The key question is determining the likelihood that a k-mer "b" matches k-mer "a" in at least "r" positions out of "k". The conclusion emphasizes that without specific numerical data, an exact probability cannot be established. This analysis is crucial for understanding sequence similarities in protein research.
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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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