Question

suppose that 1% of a large population carries anti-bodies to hiv in their blood. we choose a personfrom this population at random. given that the eiatest is positive, find the probability that the personhas the antibody. show your work.

Answer 1

The probability that a person has the antibody given a positive EIA test is 18.8%.

We find the probability by applying Bayes' Theorem. Bayes' theorem allows us to calculate the probability of event A (having antibodies) happening given event B (positive EIA test) already occurred:

P(Antibody | Positive Test) = P(Positive Test | Antibody) * P(Antibody) / P(Positive Test)

P(Positive Test) = P(Positive Test | Antibody) * P(Antibody) + P(Positive Test | No Antibody) * P(No Antibody)

We the Substitute the known values:

P(Positive Test) = (0.95 * 0.01) + (0.05 * 0.99)

= 0.0505

The final probability is found by substituting all the values into the Bayes' theorem equation:

P(Antibody | Positive Test) = (0.95 * 0.01) / 0.0505

= 0.188