1. The problem is to find the probability that a person has the disease given a positive test result, using the sensitivity, specificity, and prevalence. 2. We use Bayes' theorem: $$P(D|T) = \frac{P(T|D) \times P(D)}{P(T|D) \times P(D) + P(T|\neg D) \times P(\neg D)}$$ where: - $P(D)$ is the prevalence (probability of disease) = 0.02 - $P(\neg D)$ is the probability of no disease = 1 - 0.02 = 0.98 - $P(T|D)$ is sensitivity = 0.95 - $P(T|\neg D)$ is false positive rate = 1 - specificity = 1 - 0.90 = 0.10 3. Substitute values: $$P(D|T) = \frac{0.95 \times 0.02}{0.95 \times 0.02 + 0.10 \times 0.98}$$ 4. Calculate numerator and denominator: $$= \frac{0.019}{0.019 + 0.098} = \frac{0.019}{0.117}$$ 5. Simplify fraction: $$= \frac{\cancel{0.019}}{\cancel{0.117}} = 0.1624$$ (approx.) 6. So, the probability that a person has the disease given a positive test is approximately 16.24%. This matches the answer option approx. 16%.