Proceedings of the Annual Meeting of the Cognitive Science Society

People overestimate the conjunctive probability of independent events (Bar Hillel, 1973). We examined conjunctive per-formance in a task involving motor uncertainty and binomial sampling. Human probabilistic judgment is typically near-optimal with either of these sources of uncertainty alone. Four subjects attempted to earn rewards by reaching to circulartargets. They chose between a single smaller target and one of N larger targets. Hitting the single target always earned areward but only one on the N larger targets was rewarded: they chose between P[Smaller] and the conjunctive probability(1/N)*P[Larger] as we varied N and the sizes of the targets. The ideal observer should be indifferent when P[Smaller] =(1/N)*P[Larger]. We also asked observers to estimate the probability of hitting targets of different sizes to verify that theycould do so accurately. Remarkably, three out of four observers ignored numerosity N in their preferences.