True positive
$P(\text{have the disease and tests positive}) = \frac{1}{10,000}(0.99)$
$P(\text{have the disease and tests positive}) = 0.000\,099$
False positive
$P(\text{healthy and tests positive}) = \frac{9,999}{10,000}(0.02)$
$P(\text{healthy and tests positive}) = 0.019\,998$
Tests positive
$\begin{align}
P(\text{tests positive}) = & P(\text{have the disease and tests positive}) \\
& + P(\text{healthy and tests positive})
\end{align}$
$P(\text{tests positive}) = 0.020\,097$
Somebody is healthy given that they tests positive
$P(\text{healthy} \mid \text{tests positive}) = \dfrac{P(\text{healthy and tests positive})}{P(\text{tests positive})}$
$P(\text{healthy} \mid \text{tests positive}) = \dfrac{0.019\,998}{0.020\,097}$
$P(\text{healthy} \mid \text{tests positive}) = 99.51\%$ ← answer
