Computer simulations and 2 experiments demonstrate the ultimate sampling dilemma, which constitutes a serious obstacle to inductive inferences in a probabilistic world. Participants were asked to take the role of a manager who is to make purchasing decisions based on positive versus negative feedback about 3 providers in 2 different product domains. When information sampling (from a computerized database) was over, they had to make inferences about actual differences in the database from which the sample was drawn (e.g., about the actual superiority of different providers, or about the most likely origins of negatively valenced products). The ultimate sampling dilemma consists in a forced choice between 2 search strategies that both have their advantages and their drawbacks: natural sampling and deliberate sampling of information relevant to the inference task. Both strategies leave the sample unbiased for specific inferences but create errors or biases for other inferences.