Path.GetRandomFileName
returns a crypto-strong string of 11 random chars. It is built of 8 chars + dot + 3 chars, like: "b253i5vu.psf". A char can be a lowercase letter or a number between 0 and 5. So the number of possible strings is 32^11.
My question have been already asked here and here, but the answers are all wrong, because:
They say that the chance for a collision is some X value, while in fact it depends on how many files there are already in the directory. So, for ex., if you have a dir with 100,000 files that were generated with Path.GetRandomFileName, the chance for a collision is higher then for a dir with 1000 files.
They don't take into account the Birthday Problem.
If possible, I appreciate if you can present the formula in a way which is easy to use for people who don't have university-level math knowledge, or if you can give instructions of how to calculate it for a specific value (for ex., if the dir has 1000 files).