Measures of the probability of all unobserved species are applied to the problem of assessing the adequacy of a search for a global maximum using random starting points. The measures, as used here, estimate the probability that an iterative algorithm using a randomly selected starting point will find a solution not observed in previous random starting points. The probability of an unobserved global maximum is less than or equal to this probability. We used these measures to evaluate the adequacy of our search procedure for the maximum likelihood estimates of the parameters of a mixture of two normals. These measures indicated that for most problems generated there was little chance that there were unobserved domains of convergence. Occasional problems, however, had appreciable estimated probabilities. In such problems, examination of the data suggested regions where a more focused search for unobserved domains of convergence was warranted.