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 absent if the test result is negative?
A)0.9553
B)0.8994
C)0.9999
D)0.9762

Question

Quizplus · Accepted Answer

The probability that the disease is absent if the test result is negative can be calculated using the formula for conditional probability. Given that the disease prevalence is 0.5% (or 0.005) and the test has a 99% sensitivity (or 0.99 probability of correctly identifying the disease when it is present) and a 96% specificity (or 0.96 probability of correctly identifying when the disease is not present, since it has a 4% false-positive rate), we can calculate the probability of not having the disease given a negative test result. The high specificity and low disease prevalence contribute to a very high probability of truly not having the disease if the test is negative, which is very close to 1 (or 100%).

Disco Fever Is Randomly Found in One Half of One