Understanding risk

It is often argued that humans have a hard time understanding probability, and the proof if is something like this:

Does all this mean that humans will perpetually remain stuck when it comes to risk and probability? Possibly not, but we have to be careful. That was the message of Gerd Gigerenzer, who helps train decision makers in how to evaluate probabilities. Gigerenzer consistently noted that language was important when it comes to dealing with probabilities.

The most compelling example he gave was one he used when working in medical education. He described the probabilities associated with a breast cancer test: one percent of women tested have the disease, and the test is 90 percent accurate, with a nine percent false positive rate. With all that information, what do you tell a woman who tests positive about the likelihood they have the disease? For a lot of people in medicine, the question leaves them stumped;

The failure here is with whoever formulated such a hopelessly ambiguous question.
The key clue here is the nine percent false positive rate is supposed to mean that 9% of all women taking the test give a positive result without having the disease. It does not mean that 9% of the positives are false.

The 90% accuracy is even more confusing. If the test were always negative, then it would be 99% accurate, the way this rate is computed. The figure is only there to confuse you.