Second, as stated in Chapter 4, a match indicates that the two bullets probably came from the same source or from compositionally indistinguishable volumes of lead, of which thousands exist from different periods, for different types of bullets, for different manufacturers, and so on, not just 365. Even if interest lay in the probability of a match between any two bullets, the above calculation with N = 5,000 and n + 1 = 6 or 23 or 55 bullets yields much smaller probabilities of 0.003, 0.0494, and 0.2578, respectively.
Third, if bullets manufactured at the same time tend to appear in the same box, and such boxes tend to be distributed in geographically nondispersed locations, the n potential suspect bullets are not independent, as the n persons’ birthdays in the birthday problem are assumed to be.
We conclude that this analogy with the birthday problem does not apply.
1. Chung, K.-L. Elementary Probability Theory with Stochastic Processes, 2nd Ed., Springer-Verlag: New York, NY, 1975; p 63.