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 comes back negative regardless of whether the disease is present?
A)0.9553
B)0.8994
C)0.9999
D)0.9762

Question

Quizplus · Accepted Answer

The probability of a negative test result is the sum of the probability of a true negative and the probability of a false negative. The probability of not having the disease is 0.995, and the probability of a true negative is 0.995 * 0.96 = 0.9552. The probability of having the disease is 0.005, and the probability of a false negative is 0.005 * 0.01 = 0.00005. Adding these gives 0.9552 + 0.00005 = 0.95525, which rounds to 0.9553.

Disco Fever Is Randomly Found in One Half of One