Summary: Considered is the set-up of sampling from a finite population of \(N\) (known) units divided into \(k\) (unknown) mutually exclusive and exhaustive categories, the \(i\)th category possessing \(N_ i\) (unknown) units, \(1\leq i\leq k\). As and when sampling is terminated, some categories may remain undiscovered. A quantity of interest is the probability of discovering a new category when an additional draw is made. We address the problem of estimation of this unknown probability and also that of more general parametric functions. Simple random sampling (with/without replacement) is discussed.