Wolpert argues that even experts can be irrational and uses a brain teaser about probability to illustrate this: a disease affects 1 per cent of people. The probability that a test will detect it is 80 per cent but has a 10 per cent false alarm rate. Given a positive test result, what is the probability that a patient has the disease?
Although even Harvard medical school staff have difficulties with this, most undergraduates readily provide the correct answer to the same problem described with frequencies because then it is easy to "see" the answer. Imagine 1,000 people (think of a 100 x 10 grid). Only 10 people will have the disease and eight of these a positive test. Tests on the other 990 will give 99 false positives. The answer is clear: eight of the 107 with a positive test have the disease.
There are reports of surgeons in the US performing "preventative mastectomies" on the basis of faulty reasoning with probability of cancer. There are easier ways of talking about risks than by using baffling mathematical nomenclature.