**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*