# Probability Without Counting and Dividing: A Fresh Computational Perspective

- Thomas Shultz, Psychology, McGill University, Montreal, Quebec, Canada
- Ardavan S. Nobandegani, Psychology, McGill University, Montreal, Quebec, Canada

**Abstract**Recent experiments show that preverbal infants can reason probabilistically. This raises a deep puzzle because infants lack the counting and dividing abilities presumably required to compute probabilities. In the standard way of computing probabilities, they would have to count or accurately estimate large frequencies and divide those values by their total. Here, we present a novel neural-network model that learns and uses probability distributions without explicit counting or dividing. Probability distributions emerge naturally from neural-network learning of event sequences, providing a computationally sufficient explanation of how infants could succeed at probabilistic reasoning. Several alternative explanations are discussed and ruled out. Our work bears on several other active literatures, and it suggests an effective way to integrate Bayesian and neural-network approaches to cognition.