Question

A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.94. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.05. It is estimated that 6% of the population who take this test have the disease. (Round your answers to three decimal places.) (a) If the test administered to an individual is positive, what is the probability that the person actually has the disease? (b) If an individual takes the test twice and the test is positive both times, what is the probability that the person actually has the disease? (Assume that the tests are independent.)

Answer 1

Let us denote the events :

A : a randomly selected person has the disease

B : a randomly selected person tested positive

Given

a) If the test administered to an individual is positive, the probability that the person actually has the disease is

(Bayes' Theorem)