Uncertainty in clinical encounters is inevitable and despite this uncertainty clinicians must still work with patients to make diagnostic and treatment decisions. Explicit diagnostic reasoning based on probabilities will optimise information in relation to uncertainty. In clinical diagnostic encounters, there is often pre-existing information that reflects the probability any particular patient has a disease. Diagnostic testing provides extra information that refines diagnostic probabilities. However, in general diagnostic tests will be positive in most, but not all cases of disease (sensitivity) and may not be negative in all cases of disease absence (specificity). Bayes rule is an arithmetic method of using diagnostic testing information to refine diagnostic probabilities. In this method, when probabilities are converted to odds, multiplication of the odds of disease before diagnostic testing, by the positive likelihood ratio (LR+), the sensitivity of a test divided by 1 minus the specificity refines the probability of a particular diagnosis. Similar arithmetic applies to the probability of not having a disease, where the negative likelihood ratio is the specificity divided by 1 minus the sensitivity. A useful diagnostic test is one where the LR+ is greater than 5–10. This can be clarified by creating a contingency table for hypothetical groups of patients in relation to true disease prevalence and test performance predicted by sensitivity and specificity. Most screening tests in populations with a low prevalence of disease have a very high ratio of false positive results to true positive results, which can also be illustrated by contingency tables.