In the unfortunate event of getting sick and having to seek professional care, consumers of healtcare often have to make a choice between different options for diagnostic interventions or medical treatments. As Gaissmaier and Gigerenzer point out, choosing the right option basically boils down to weighing the different statistical risks or chances (probabilities) involved in the treatment options or diagnostic interventions.
In order for a consumer to come to a "right" decision they have to be able to understand and calculate risks (probabilities) correctly. Normally this is not very intensively taught in schools leading to statistical illiteracy or innumeracy, or a life long disability to calculate risks, chances, or probabilities correctly. So the healthcare consumer dependends on the care provider for doing the calculation and weighing of the probabilities for him, thus rendering the concept of shared decision making with equal partners not practical.
As the authors further point out, not even the healthcare providers always get the calculation right. Be brave and give it a try:
For those who want to find the correct answer, it is just a straight forward application of Bayes' theorem.