Your radio wakes you up to a gloriously sunny day, but you soon learn that the day will be anything but sunny as “Station A” announces their day’s forecast:

Station A: By mid-morning the sky will become completely overcast with a 70 percent chance of severe thunderstorms for most of the afternoon.

That’s particularly bad news because you’re hosting your family’s annual picnic this afternoon. You quickly flip the radio dial to “Station B” and you hear a slightly different forecast:

Station B: Today’s temperature will be in the low 80s with heavily overcast skies for most of the afternoon with zero percent chance of rain.

Always the optimist, you count on Station B’s forecast and go ahead with your picnic as planned, which is lucky you did because it never did rain … not a single drop. Based on the two forecasts which of the following statements is most accurate:

o    A. Station A’s forecast was wrong and Station B’s forecast was right.

o    B. Both Station A and Station B’s forecasts were right.

o    C. Neither Station A nor Station B was wrong.

Answer:

Although the correct answer is C, most people choose answer A.

In fact, this simple mistake is so common that even sophisticated thinkers and people well versed in statistical forecasting fall for it.

If the forecast said there was a 70 percent chance of rain and it rains, most people think the forecast was right; and if it doesn’t rain, they think it was wrong.

This sort of primal thinking goes a long way to explaining why so many people have a poor grasp of probability. To grasp the meaning of “a 70 percent chance of rain” we have to understand that rain may or may not happen and that over 100 days on which we forecast chances of rain, if our forecasts are good, it should rain on 70 percent of them and be dry on the rest. Nothing could be further removed from our natural inclination to think, “It will rain” or “It won’t rain” – or, if you insist, “Maybe it will rain.”

People often make the mistake of looking at which side of “maybe” – 50 percent –  the probability is on, and they’ll base their decisions on that while completely ignoring the distinct possibility that (in this case) there’s was a 30 percent chance of the other option occurring.

Robert Rubin, the former Secretary of the U.S. Treasury, told how he and his then deputy, Larry Summers, would often be frustrated when they briefed top policy makers in the White House and Congress because people would treat an 80 percent probability that something would happen as a certainty that it would. “You almost had to pound the table, to say ‘yes there’s a high probability but this also might not happen,’” Rubin said. “But the way people think, they seem to translate a high probability into ‘this will happen.’” And yet, if we were to take these presumably educated, accomplished people out of that context, sit them down in a classroom, and tell them that the statement “There is an 80 percent chance that something will happen” means there is a 20 percent chance it won’t, they would surely roll their eyes and say, “That’s obvious.” But outside of a classroom, away from abstractions, when dealing with real issues, these educated, accomplished people reverted to the intuitive.

Only when the probabilities were closer to even did they easily grasp that the outcome may or may not happen, Rubin said. “If you say something is 60/40, people kind of get the idea.” (1)

1. Turner, M. E., Pratkanis, A. R., “Twenty-Five Years of Groupthink Theory and Research: Lessons from the Evaluation of a Theory,” Organizational Behavior and Human Decision Processes, 1998, 73(2/3): 105–115