A test for an infection is positive for 95% of the people who have it…

Step 1. Town M. Infected and positive: $0.02 \times 0.95 = 0.019$. Healthy and positive: $0.98 \times 0.08 = 0.0784$. So $P = \dfrac{0.019}{0.019 + 0.0784} = \dfrac{0.019}{0.0974} \approx 0.1951$.

Step 2. Town N. Infected and positive: $0.2 \times 0.95 = 0.19$. Healthy and positive: $0.8 \times 0.08 = 0.064$. So $P = \dfrac{0.19}{0.254} \approx 0.748$.

What it means. The same test and the same result mean very different things in the two towns. The base rate in town N is ten times as large, and the chance after a positive result is almost four times as large.