  When estimating a proportion and only a sample of triplets is given,
dependencies within the triplets are to be accounted for. Without assuming a
distribution for the success count of the triplet, together with the
proportion, as second and third parameter the correlations of 1st and 2nd order
enter the model. We apply maximum likelihood estimation, and derive consistency
by using that the triplet count is multinomially distributed, combined with the
continuous mapping theorem. The asymptotic normality follows with the
delta-method, resulting in closed-form expressions for the standard errors. As
application we study caries prevalence of pre-school children from a sample to
nursing schools. We compare the standard errors with those for assuming
erroneously independence within the nursing schools. As to be suspected, the
design `inflates' the standard error markedly.
