When dealing with the problem of obtaining information concerning consumer preferences for two competing brands of a product, one would like to assume that the consumers sampled can actually distinguish between the two brands. Often this is not the case and we have combined the standard triangle test of sensory perception with a preference test in order to obtain information concerning the consumers' ability to distinguish between the two brands. Assuming an underlying multinomial distribution, the maximum likelihood estimators (MLE) of the conditional probability that a person prefers brand A given that he can discriminate between the two products is then obtained. The estimator obtained is a ratio of linear combinations of observed multinomial proportions. The variability of this estimator is assessed by means of the jackknife statistic, the asymptotic variance of the MLE, and Monte Carlo studies. Application of the results obtained to taste test involving two brands of potato chips is discussed.