Rapid HIV tests allow for quick diagnosis without expensive laboratory equipment. However, their efficacy has been called into question. In a population of 1517 tested individuals in Uganda, 4 had HIV but tested negative (false negatives), 166 had HIV and tested positive, 129 did not have HIV but tested positive (false positives), and 1218 did not have HIV and tested negative (Gray et al. 2007). Assume that these proportions represent the probabilities of the corresponding outcomes.

a. What was the probability of a false positive (also called the false-positive rate)?

b. What was the false-negative rate?

c. If a randomly sampled individual from this population tests positive on a rapid test, what is the probability that he or she has HIV?