Chance of random generated string of being in a set with strings Given a finite set of m strings with length n. Each position of the string can be one of k possibilites for a character.
If I now generate such a string what is the chance of it being in the set?
 A: The probability is $m/k^n$.
Answering the harder question asked in the comment:

What if each of the characters in the string has a probability
  assigned to it. Like lets say I have a software that scans a string
  and gives back the string with each character having a probability
  assigned to it measuring the chance it was scanned correctly. This
  uncertainty would change the probability of the string being in the
  set. How do I put this uncertainty for each character to the
  calculation?

Or, rather, not answering, since there is no easy answer. 
If the probability of a bad character scan is $p$, independent from character to character, then it's not hard to calculate the probability that $j$ of the $n$ characters are wrong. But without more information about the set $V$ of valid strings you are looking for you can't calculate the probability that the misread string is in $V$. That will depend on how often random changes of strings in $V$ stay in $V$.
Some of what you are asking about may be addressed by coding theory. 
You may get more help if you submit a new question with much more context about your use case.
