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 test result is positive?
A)0.0056
B)0.0523
C)0.0448
D)0.1106

Question

Quizplus · Accepted Answer

Using Bayes' theorem, we have:

P(DF | T+) = P(T+ | DF) * P(DF) / [P(T+ | DF) * P(DF) + P(T+ | ~DF) * P(~DF)]
where
DF = Disco Fever
T+ = Test positive

We know P(DF) = 0.005 (given in the question)
P(T+ | DF) = 0.99 (given in the question, the test is 99% effective in detecting Disco Fever)
P(T+ | ~DF) = 0.04 (given in the question, the test yields a false positive in 4% of cases where the disease is not present)
P(~DF) = 1 - P(DF) = 0.995

Plugging in the values, we get:

P(DF | T+) = 0.99 * 0.005 / [0.99 * 0.005 + 0.04 * 0.995]
= 0.0448

Therefore, the probability that the test result is positive is 0.0448, or approximately 4.48%. The closest answer choice is C.

Disco Fever Is Randomly Found in One Half of One