  The present work analyzes the redundancy of sets of combinatorial objects
produced by a weighted random generation algorithm proposed by Denise et al.
This scheme associates weights to the terminals symbols of a weighted
context-free grammar, extends this weight definition multiplicatively on words,
and draws words of length $n$ with probability proportional their weight. We
investigate the level of redundancy within a sample of $k$ word, the proportion
of the total probability covered by $k$ words (coverage), the time (number of
generations) of the first collision, and the time of the full collection. For
these four questions, we use an analytic urn analogy to derive asymptotic
estimates and/or polynomially computable exact forms. We illustrate these tools
by an analysis of an RNA secondary structure statistical sampling algorithm
introduced by Ding et al.
