# Testing human use of probability in a visuo-motor conjunction task

- Laurence Maloney, Psychology, New York University, New York, New York, United States
- Jinsoo Kim, Psychology, New York University, New York, New York, United States
- Keiji Ota, Psychology, New York University, New York, New York, United States

**Abstract**People overestimate the conjunctive probability of independent events (Bar Hillel, 1973). We examined conjunctive performance 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 circular targets. They chose between a single smaller target and one of N larger targets. Hitting the single target always earned a reward 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 they could do so accurately. Remarkably, three out of four observers ignored numerosity N in their preferences.