Because of baseline fluctuation in an instrumental analysis, a purity test can overlook an illegitimate drug which contains an undesirable substance in more amount than a prescribed reference value. This paper proposes a probability theory to predict the lowest (average) signal, E[Y2], of the substance which can be discriminated from the (average) reference signal, E[Y1], with a high probability (here, 95%) in liquid chromatography (LC). The difference between the lowest signal and reference signal, E[Y2]-E[Y1] (> 0), is referred to here as a discrimination limit. The repetition of experiments to estimate the standard deviation of measurements is unnecessary for the probability theory, but a mathematical treatment of instrumental baselines (Fourier transform, etc.) is essential. The Monte Carlo simulation is carried out in which the reference signal and predicted signal for the discrimination limit are overlaid randomly 5000 times on real LC baselines. The result is satisfactory: the observed probability for the right answer is 94.3 or 94.8%; the theoretical one is 95%. The normality of the measurement distribution is examined for LC and capillary electrophoresis to verify the fundamental assumption of the proposed theory.