Question

Results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources) showed 337 subjects with positive test results including 2 false positive results. There were 1,163 negative results, including 10 false negative results. What is the probability that a randomly selected subject had no hepatitis C?

11.

Answer 1

The probability that a randomly selected subject had no hepatitis C is P=0.77.

Explanation:

To calculate the probability of randomly selecting a subject and that he or she has no hepeatitis C can be calculated as the proportion of subjects with true negative results out of the total subjects tested.

The true negative results include the true negative and the false positives.

There are 337 positive results (P) and 1163 negative results (N).

The false positives (FP) are 2.

The true positives (TP) are 337-2=335.

The false negatives (FN) are 10.

The true negatives (TN) are 1163-10=1153.

Then we can calculate the proportion as:

`p=(TN+FP)/(P+N)=(1153+2)/(337+1163)=(1155)/(1500)=0.77`

The probability that a randomly selected subject had no hepatitis C is P=0.77.