Understanding probability is key to understanding uncertainty, quantifying evidence for effects, and making decisions in the face of uncertainty. In teaching many clinicians over many years I’ve found the lack of sufficient understanding of probability results in misunderstanding probabilistic diagnosis, sensitivity, specificity, prevalence, probabilistic prognostication, p-values, and number needed to treat. The problem is made more acute when patients have even more difficulties with probability than their physicians. Some patients and physicians even believe that probabilities do not apply to individuals, when in fact “playing the odds” is how we make most of our important decisions. Poker players and sports gamblers can master probability, so why can’t everyone else? Some persons misinterpret a probability of disease of 0.2 as saying “I’m the one in five who will be lucky” even though he acts appropriately when wagering on a football game.

There seems to be three general areas that users of probability need to understand:

- Given that a probability has been correctly stated, what does that probability mean?
- What is conditional probability, what do you condition on, and how do you compute it? [I’ve seen more physician confusion on conditioning than on any other aspect of probability, with many physicians not even clear on when they are conditioning on unknowable conditions, or on the future. Even more common is the use of incomplete conditioning, e.g. computing the risk of disease given a patient is > 60 years old when you already know the patient is 61 years old.]
- How to operate on probabilities using the laws of probability to reverse the conditioning, compute probabilities of unions and intersections of conditions, and understand independence of events.

An attempt at a crash course in probability is in Section 3.8 of BBR. Suggestions for improving that section are most welcomed. The short section introduces the fundamentally different but all valid meanings of probability (limiting relative frequencies, subjective, etc.).

What suggestions do you have for resources and approaches for teaching probability to physicians and patients?