Your use of statistics is somewhat misguided. The images that people look at are not remotely random, and one cannot assume that they are. pengvado is correct in saying that in raw bitmaps (particularly of few-colored things), there is a high probability of getting identical bytes. If you want to suggest "simple" methods to check if two files are identical before doing full MD5s, go ahead. (Filesize, first few bytes, random byte, and CRCs are all good suggestions.) Considering the OP hinted at a hashing method, please keep in mind the birthday paradox: remember that collisions among many objects are much likelier than those among just two. (Incidentally, your equations are missing a 1- on the LHS and may be more simply written as 1/256 and 1/256^2)
To summarize: Equally sized and colored Canadian and Chinese flags would have about a 50% chance of differing at a random byte (they are mostly the same shade of red). Similarly with United States and Japanese flags (they share a lot of white).
++pengvado.
In reply to Re^4: Comparing images
by kaif
in thread Comparing images
by Anonymous Monk
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