Question

A test for syphilis gives a positive result with probability 0.98 when tested on a person who has the disease. The test gives a negative result with probability 0.9 when tested on a person who does not have the disease. Assume that 3% of a society has the disease, and compute the following probabilities in the order they are asked. Note that for each individual there are two disease status(disease, no disease) and two types of test results(positive, negative). (a) (0.5 point) Compute the probability that an individual has the disease and has a positive test result. Explain your computation. (b) (0.5 point) Compute the probability

Answer 1

The probability that an individual has the disease and has a positive test result is:

9.8%.

Explanation:

Probability of a true positive result for a test of syphilis = 0.98 or 98%

Probability of a false negative result for a test of syphilis = 0.02 or 2% (100 - 98)

Probability of a true negative result for a test of syphilis = 0.9 or 90%

Probability of a false negative result for a test of syphilis = 0.1 or 10% (100 - 90)

Therefore, the probability that an individual has the disease and has a positive test result = 0.98 * 0.1 = 0.098 = 9.8%