Disco Fever is randomly found in one half of one percent of the general population.Testing a swatch of clothing for the presence of polyester is 99% effective in detecting the presence of this disease.The test also yields a false-positive in 4% of the cases where the disease is not present.What is the probability that the disease is present if the test result comes back positive?
A)0.1106
B)0.8894
C)0.9600
D)0.0400

Question

Quizplus · Accepted Answer

To solve this, we use Bayes' theorem. Let's denote D as having the disease and + as testing positive. We're looking for P(D|+), the probability of having the disease given a positive test result.P(D|+) = [P(+|D) * P(D)] / [P(+|D) * P(D) + P(+|¬D) * P(¬D)]Given:- P(+|D) = 0.99 (probability of testing positive given the disease)- P(D) = 0.005 (probability of having the disease, 0.5%)- P(+|¬D) = 0.04 (probability of testing positive given no disease)- P(¬D) = 0.995 (probability of not having the disease, 100% - 0.5%)Plugging in the numbers:P(D|+) = (0.99 * 0.005) / (0.99 * 0.005 + 0.04 * 0.995) = 0.00495 / (0.00495 + 0.0398) ≈ 0.1106

Disco Fever Is Randomly Found in One Half of One