You have two sequences, a long one and a short one. The short one is 3 characters long, the long one is 40 characters long. They are comprised of characters from the latin alphabet (each char can be one of 26 possible chars). What is the probability of the shorter sequence occurring in the longer sequence? Keep everything symbolic right up to the end.
Let's denote the short sequence as S and the long sequence as L. The short sequence S has a length of 3 characters, while the long sequence L has a length of 40 characters. We want to find the probability of S occurring in L.
There are 26 possible characters for each position in both sequences, and there are (40-3+1) = 38 possible positions in the long sequence where the short sequence could be placed.
Let's compute the probability of the short sequence occurring at a specific position in the long sequence. Since there are 26 possible characters for each position and the characters are assumed to be independent, the probability of the sh