Method 1: Let’s design a contingency table to illustrate the situation among 1000 people.

• The disease prevalence is 0.1%, so among 1000 people, 1 is infected.
• 99 of 100 affected people are detected by the test, so the test sensitivity is 99%. Thus, the number of true positive is 1*0.99 ˜ 1
• 98 of 100 non-infected people are correctly classified as healthy, so the test specificity is 98%. Thus, the number of true negative is 999 * 0.98 ˜ 979
• Consequently, the number of false positive is 999-979=20
• Finally, the test positive predictive values is PPV = P (Barking madness+ | Blood test+) = 1 / 21 ˜ 4.7%

Conclusion
There is only a 4.7% probability that the positive test comes from a truly infected individual, and a bigger than 95% probability that it is a false-positive result.