In the book Elements of Information Theory (p.446), it is stated:
...although there are some simple sequences, most sequences do not have simple descriptions. Similarly, most integers are not simple. Hence, if we draw a sequence at random, we are likely to draw a complex sequence. The next theorem shows that the probability that a sequence can be compressed by more than k bits is no greater than 2−k.
[snip latex Theorem and Proof]
Thus, most sequences have a complexity close to their length. For example, the fraction of sequences of length n that have complexity less than n − 5 is less than 1/32.
So, the answer I'm looking for looks something like:
For some given set and string length, for a random set of random strings, the number of compressible strings in that set will be on average X percent of that set.
Where X may be 0.0001% or 0.00002193487% or 0.000000009% or something more specific.