Western Governors University (WGU) DTAN3100 D491 Introduction to Analytics Practice Exam

To determine the probability that John actually has swine flu after testing positive, we must consider the principles of conditional probability and the concepts of sensitivity and specificity of the test, as well as the prevalence of the disease in the population.

When a test is conducted, it can produce true positive results (indicating a person has the disease when they actually do) and false positive results (indicating a person has the disease when they do not). The probability of a positive test result being a true positive is influenced by the actual prevalence of the disease and the reliability of the test.

In this scenario, the correct choice indicates that the probability of having swine flu after a positive test result is extremely low. This can occur in contexts where the disease is rare within a population, combined with a test that may have a considerable false positive rate. When the prevalence of swine flu is very low, even with a positive test result, the likelihood that it is a true positive diminishes significantly.

Using Bayes’ theorem, which calculates the posterior probability based on prior knowledge and the likelihood of the test results, can show that even with a positive test, the actual chance of having the disease may remain small, particularly if many people who do not have the disease