 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $G$ denote carrying the <gene> and $+$ a positive result. The <law of total probability> gives
$$
\boxed{P(+)=P(+\mid G)P(G)+P(+\mid G^c)P(G^c)=0.99(0.001)+0.05(0.999)=0.05094\simeq0.0509.}
$$
The last value is to three significant figures. The much larger non-carrier population contributes most of the positive tests in this mathematical model.

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