Reasoning with frequencies vs. reasoning with probabilities
Though it's frustrating that we humans seem so poorly designed for explicit probabilistic reasoning, we can often dramatically improve our performance on these sorts of tasks with a quick fix: just translate probabilities into frequencies.
Recently, Gigerenzer (1994) hypothesized that humans reason better when information is phrased in terms of relative frequencies, instead of probabilities, because we were only exposed to frequency data in the ancestral environment (e.g., 'I've found good hunting here in the past on 6 out of 10 visits').
He rewrote the conjunction fallacy task so that it didn’t mention probabilities, and with this alternate phrasing, only 13% of subjects committed the conjunction fallacy. That's a pretty dramatic improvement!
Bill is 34 years old. He is intelligent, but unimaginative, compulsive, and generally lifeless. In school, he was strong in mathematics but weak in social studies and humanities.
There are 200 people who fit the description above. How many of them are:
Gigerenzer, G. (1994). Why the distinction between single-event probabilities and frequencies is important for psychology (and vice versa). In G. Wright and P. Ayton, eds., Subjective Probability. New York: John Wiley.