If, for example, a forecast calls for a 20 percent chance of rain, many people think it means that it will rain over 20 percent of the area covered by the forecast. Others think it will rain for 20 percent of the time, said Susan Joslyn, a cognitive psychologist at the University of Washington who conducted the study.
Of course, how the article should really be titled is simply "Probability is Misunderstood by Many". I see the same -- dare I say stunning -- difficulty that enormous numbers of college students have in interpreting the most basic probability statements. Unfortunately, in the classes that I teach probability is never more than a quick two-week building-block on the way to something else (either in a survey class, fundamentals of inferential statistics, etc.). Part of me wishes we could give a whole semester course in probability (and basic game theory?) to everyone, but I know there's no room for that in the basic curriculum.
Having seen the difficulty, I've tried to emphasize the interpretation process more in later semesters, and tend to run into more and more resistance against it. Even students who are in the habit of happily crunching on formulas and churning out numerical solutions can be vaguely frustrated and unhappy at being asked what the numbers mean.
This is one where I find it really hard to empathize with the students on the issue (that being rare for me), and I almost can't begin to imagine where I need to start if I get an incredulous response as to how I knew that 75% was "a good bet" if I mention that in passing. Perhaps just growing up in an environment where I was personally steeped in games as recreation every day for decades (chess, craps, Monopoly, Risk, poker, D&D -- see here for more) marinated the fundamental idea of probability into my brain in a way that can't be shared in a class lecture.
Anyway, some people have suggested that statistics needs to be taught to everyone functioning in a modern society. Even more fundamental (after all, it's foundational to statistics) would be getting the majority of people to have a sense for probability in their gut, because most people currently do not. I'd hypothesize that psychological experiments like those at U. Washington have promise of cornering the precise way that our brains are fundamentally irrational -- that math so simple could be so bewildering in practice, suggests a deep limitation (or variant prioritization) in our cognitive abilities.