We present a computational model of the representativeness heuristic. This model is trained on the entire English language Wikipedia corpus, and is able to use representativeness to answer questions spanning a very large domain of knowledge. Our trained model mimics human behavior by generating the probabilistic fallacies associated with the representativeness heuristic. It also, however, achieves a high rate of accuracy on unstructured judgment problems, obtained from large quiz databases and from the popular game show Who Wants to be a Millionaire?. Our results show how highly simplistic cognitive processes, known to be responsible for some of the most robust and pervasive judgment biases, can be used to generate the type of flexible, sophisticated, high-level cognition observed in human decision makers.