In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring.
[4] The correct probability of malignancy given a positive test result as stated above is 7.5%, derived via Bayes' theorem: Other examples of confusion include: For other errors in conditional probability, see the Monty Hall problem and the base rate fallacy.
In order to identify individuals having a serious disease in an early curable form, one may consider screening a large group of people.
While the benefits are obvious, an argument against such screenings is the disturbance caused by false positive screening results: If a person not having the disease is incorrectly found to have it by the initial test, they will most likely be distressed, and even if they subsequently take a more careful test and are told they are well, their lives may still be affected negatively.
Choosing an individual at random, Suppose that when the screening test is applied to a person not having the disease, there is a 1% chance of getting a false positive result (and hence 99% chance of getting a true negative result, a number known as the specificity of the test), i.e.