This article introduces the concept of a prediction interval in a gambling context.

Rolling dice and tossing coins can still be used to teach probability even if students know (or think they know) what happens in these experiments. This article considers many simple variations of these experiments which are interesting, potentially enjoyable and challenging. Using these variations can cause students (and teachers) to think again…

Pigeons pecked left versus right keys contingent upon the color presented at 1 of those locations. Spatial-response latencies were shorter when the color appeared at the same location as the required response than at the opposite location. This Simon effect occurred when the stimulus on the alternative key was constant, varied from trial to trial,…

Models of attentional control usually describe online shifts in control settings that accommodate changing task demands. The current studies suggest that online control over distractor exclusion--a core component of visual selection--can be accomplished without online shifts in top-down settings. Measurements of target discrimination accuracy…

When forecasters and decision makers describe uncertain events using verbal probability terms, there is a risk of miscommunication because people use different probability phrases and interpret them in different ways. In an effort to facilitate the communication process, the authors investigated various ways of converting the forecasters' verbal…

The traditional approach to expressing cumulants in terms of moments is by expansion of the cumulant generating function which is represented as an embedded power series of the moments. The moments are then obtained in terms of cumulants through successive reverse substitutions. In this note we demonstrate how cumulant-moment relations are…

The author describes a card trick that failed when he tried it with the student chapter at his university. Computations show that the chance of this happening is about 1 in 25.

A result known as the Borel-Cantelli lemma is about probabilities of sequences of events. This article presents an example in which it appears that the hypotheses of the lemma are satisfied but the conclusion is not. The explanation of why not combines elements of probability theory, number theory, and analysis.

Selection theory requires multiple, distinct, simultaneously-actualized states. In cognition, each thought or cognitive state changes the "selection pressure" against which the next is evaluated; they are not simultaneously selected amongst. Creative thought is more a matter of honing in on a vague idea through redescribing successive iterations…

It is easy to construct pairs of sentences X, Y that lead many people to ascribe higher probability to the conjunction X-and-Y than to the conjuncts X, Y. Whether an error is thereby committed depends on reasoners' interpretation of the expressions "probability" and "and." We report two experiments designed to clarify the normative status of…

Analysis of binary choice behavior in iterated tasks with immediate feedback reveals robust deviations from maximization that can be described as indications of 3 effects: (a) a payoff variability effect, in which high payoff variability seems to move choice behavior toward random choice; (b) underweighting of rare events, in which alternatives…

Several norms for how people should assess a question's usefulness have been proposed, notably Bayesian diagnosticity, information gain (mutual information), Kullback-Liebler distance, probability gain (error minimization), and impact (absolute change). Several probabilistic models of previous experiments on categorization, covariation assessment,…

The prominent cognitive theories of probability judgment were primarily developed to explain cognitive biases rather than to account for the cognitive processes in probability judgment. In this article the authors compare 3 major theories of the processes and representations in probability judgment: the representativeness heuristic, implemented as…

Speeded perceptual classification experiments were conducted to distinguish among the predictions of exemplar-retrieval, decision-boundary, and prototype models. The key manipulation was that across conditions, individual stimuli received either probabilistic or deterministic category feedback. Regardless of the probabilistic feedback, however, an…

This article presents two methods of estimating a study's replicability that researchers should consider reporting along with their statistical significant and effect size findings. One method of estimating the replicability of the findings deals with replication in the exact same system. The second method, which may contain subjective probability…