Find the probability that somebody is healthy given that they have positive test result?

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