Pre-test probability
The proportion of people with the target disorder in the population at risk at a specific time (point prevalence) or time interval (period prevalence)
For example, the prevalence of rheumatoid arthritis in the UK is 1%
Post-test probability
The proportion of patients with that particular test result who have the target disorder
Post-test probability = post test odds / (1 + post-test odds)
Pre-test odds
The odds that the patient has the target disorder before the test is carried out
Pre-test odds = pre-test probability / (1 - pre-test probability)
Post-test odds
The odds that the patient has the target disorder after the test is carried out
Post-test odds = pre-test odds x likelihood ratio
where the likelihood ratio for a positive test result = sensitivity / (1 - specificity)
Odds are a ratio of the number of people who incur a particular outcome to the number of people who do not incur the outcome. The odds ratio may be defined as the ratio of the odds of a particular outcome with experimental treatment and that of control.
In contrast, probability is the fraction of times you'd expect to see an event in many trials. When expressed as a single number probability is always between 0 and 1. So, if we take the example of rolling a dice: