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Published online by Cambridge University Press: 14 July 2016
Consider N urns into which n balls are dropped independently with equal probability of hitting each urn and constant probability p of staying in the urn. We find the characteristic function of the joint distribution of KN and LN where KN is the number of urns that have not been hit, and LN is the number of urns where all balls have fallen through. Furthermore, we study the asymptotic distribution of (KN, LN) as n, N → ∞ at various rates.