conditional probabilities. Suppose 1% of the group suffer from the disease, and the rest are well. 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. Finally, suppose that when the test is applied to a person having the disease, there is a 1% chance of a false negative result (and 99% chance of getting a true positive result, known as the sensitivity of the test), i.e. Calculations The fraction of individuals in the whole group who are well and test negative (true negative): The fraction of individuals in the whole group who are ill and test positive (true positive): The fraction of individuals in the whole group who have false positive results: The fraction of individuals in the whole group who have false negative results: Furthermore, the fraction of individuals in the whole group who test positive: Finally, the probability that an individual actually has the disease, given that the test result is positive: Conclusion In this example, it should be easy to relate to the difference between the conditional probabilities P(positive | ill) which with the assumed probabilities is 99%, and P(ill | positive) which is 50%: the first is the probability that an individual who has the disease tests positive; the second is the probability that an individual who tests positive actually has the disease. Thus, with the probabilities picked in this example, roughly the same number of individuals receive the benefits of early treatment as are distressed by false positives; these positive and negative effects can then be considered in deciding whether to carry out the screening, or if possible whether to adjust the test criteria to decrease the number of false positives (possibly at the expense of more false negatives). See also Converse (logic) Prosecutor's fallacy References Probability fallacies Misuse of statistics zh:条件概率#条件概率谬论