E everybody thinks probabilistically, whether knowingly or not. We judge the likelihood that the barking dog will bite, that the rumor that the company is about to have a big layoff is true, that bottled water is purer than what one gets from one's kitchen faucet… The ability to think probabilistically is important for many reasons. Lack of it makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naivete, precludes intelligent assessment of risks, ensures the operation of several common biases, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, precludes critical evaluation of likelihood claims, and generally undercuts rational thinking in numerous ways.
Often we lack the kind of evidence on complex issues that would permit us to draw a conclusion that we can be certain is correct. Frequently we have to make decisions on the basis of incomplete information and we cannot be sure of their consequences. But the need to settle for incomplete and uncertain information does not mean that our reasoning and decision making must be reduced to pure guesswork. Usually information of a statistical or probabilistic sort is available, or at least there is a basis for making some assumptions about the statistical or probabilistic characteristics of a situation of interest. One who can use this type of information effectively should do better, on the average, than one who cannot.
How good are individuals at thinking probabilistically? How consistent is people's reasoning under uncertainty with the principles of probability theory and mathematical statistics? These questions have been of considerable interest to researchers and the literature on this topic is very large. The evidence that has been produced is mixed. On the one hand are numerous indications that certain basic principles are poorly understood and that reasoning that should make use of those principles often is faulty. On the other hand are some experi-