“There is a possibility of a terrorist attack.” Or, “There is a heightened possibility of a terrorist attack.”
These statements are often interpreted as, “There is a high (or very high) probability of a terrorist attack.” These are not sensible interpretations. Of course, news media do plenty to encourage such interpretations. Footage of prior attacks, police sirens, SWAT teams, helicopters, all encourage the sense of dread, which likely encourages such interpretations. On the flip side, few news reports spend any length of time on elucidating the probability of winning the ‘Megamillion Jackpot.’
Like the news media, in everyday life, people also tend to speak in terms of possibilities than probabilities. And often enough possibilities are used to denote high probabilities. And often enough incorrectly so. Sometimes because individuals are mistakenly convinced that probabilities are actually higher (most people often do not remember numbers, replacing them with impressionistic accounts consistent with imagery or their own biases) and sometimes because people are interested in heightening the drama.
Speaking in terms of possibilities also allows one the advantage of never being technically wrong, while all the time encouraging incorrect interpretations. It allows people to casually exaggerate the threat of crime, or indeed any threat they feel like exaggerating. And it allows people to underestimate the frequency of things they would rather deny: for instance, dangers of driving faster than the speed limit, or when drunk, or both. The same benefits are afforded to strategic elite actors. It allows policymakers to sound logically coherent without being so. And to sell less rational courses of action.
By possibility, we mean that something that has a chance of occurring. It doesn’t give us information as to how probable the scenario is. A little information or thinking on probabilities that can go a long way. So aim for precision. Vagueness can be a cover for insidious reasoning (including your own). Avoidable vagueness ought to be avoided.