People believe that, even in very large samples, proportions of binary signals might depart significantly from the population mean. We model this "non-belief in the Law of Large Numbers" by assuming that a person believes that proportions in any given sample might be determined by a rate different than the true rate. In prediction, a non-believer expects the distribution of signals will have fat tails. In inference, a non-believer remains uncertain and influenced by priors even after observing an arbitrarily large sample. We explore implications for beliefs and behavior in a variety of economic settings.