Abstract.—When asked to estimate the probability of outcomes of draws from a binomial population, student subjects tend to reportpvalues that clearly exceed the objective ones. The probability of specific binomial sequences was found to be even more overestimated, while the answers became much more conservative when the outcomes were grouped into a few categories. These findings were replicated in a second experiment, where the probability of heights in a male and a female student population was estimated. When the task was to estimate frequency of occurrence, instead of probability, the answers became more realistic. The conclusion is drawn that the directpestimates are relatively independent of frequency judgments, the chief determinant being the properties of the particular sample to be evaluated, irrespective of the number and probabilities of other possible sample