We have a system by which some existing members are deemed "Do not use." Unfortunately, our 'unique' identifier is only 3.65 million permutations.
-DNU is approximately 800 and growing at a rate of 1 per day. -Main population is approximately 30,000 -New and returning entrants arrive at a rate of approximately 275 per day
Given the relatively small number of permutations, how do I determine the incidence of accidental collisions where a new or returning entrant has the same identifier as a member of the DNU?
For one new entrant, the chance of a collision is just the number of existing entries divided by the number of possible IDs, here 3.65 million. You may be thinking of the birthday paradox where the chance of a collision is much higher than you think when you start with a pool of entries. If you have already verified no collision among $n$ entries and want to add the $n+1^{st}$ the collision probability is as I have said.