Most of us have to estimate probabilities every day. Whether as a trader betting on the price of a stock, a lawyer gauging a witness's reliability or a doctor pondering the accuracy of a diagnosis, we spend much of our time—consciously or not—guessing about the future based on incomplete information. Unfortunately, decades of research indicate that humans are not very good at this. Most of us, for example, tend to vastly overestimate our chances of winning the lottery, while similarly underestimating the chances that we will get divorced.

Psychologists...