A medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the test is 0.91. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.02. It is estimated that 2% of the population who take this test have the disease. If an individual takes the test twice and both times the test is positive, what is the probability that the person actually has the disease?
A) 0.481
B) 0.980
C) 0.023
D) 0.519
E) 0.977

Question

Quizplus · Accepted Answer

Using Bayes' theorem and the given probabilities, the probability that a person actually has the disease given two positive test results is approximately 0.977.

A Medical Test Has Been Designed to Detect the Presence