It is often said that something is "probably the case" or "probably not the case." The word probable comes from the Latin probabilis, meaning commendable, which itself derives from probare, to prove. Indeed, the English probable and provable have the same etymologic origin. The scientific study of probability takes the everyday notions of recommending and approving and gives them strict definitions and systematic analysis, something that narrows their focus while enhancing their power to inform. Insight into related matters is essential in advanced technological societies where experts regularly give technical advice to a public that must then decide whether or not to accept it. This may involve the development of new government policies or actions to be taken by individuals, such as submitting to a new medical treatment.

But there are other complex issues to consider. It is generally understood that probability...