There are instances, the most typical being inversion polymorphism in Drosophila, where the genotype is not directly accessible in the adult organism, but can be observed in young life-stages. In these cases, if we want to estimate genotypic probabilities in adult populations, we must examine an offspring sample from adults. In this paper we derive the maximum likelihood estimators, and their errors, for genotypic probabilities in an adult population, according to a standard protocol in which collected parents of a random sample are individually crossed with individuals of a laboratory stock with known homozygous genotype, and a fixed number of their offspring is genetically examined in young life-stages. Arnold's probabilistic model for one locus with two alleles is developed for our estimates. An optimum design which generates a minimum variance is proposed, consisting of examining a moderate offspring number (3–4) per parent. Finally, we propose maximum likelihood estimates when several samples with different numbers of parents per sample, and/or examined progeny per parent are obtained. © 1992, Cambridge University Press. All rights reserved.