The proportion solving in the first group would be independent of the proportion solving in the second group. This implies that if the proportion solving in the first group were, by chance, higher than the proportion in the population, there is no reason to suspect that the proportion solving in the second group would also be higher. Dependent proportions would be obtained if all subjects were given both problem presentations. Then, the proportion solving when the problem was presented visually would provide information about the proportion solving the problem when it was presented aurally. In sum, proportions are independent when different groups of subjects are used in the calculation of each proportion.