Answer
$0.02$%
Work Step by Step
Let $A$ be the event "adult not in a high risk group is HIV positive"
Let $A^c$ be the event "adult not in a high risk group is not HIV positive"
Let $B$ be the event "adult not in a high risk group will test positive for the HIV virus"
$P(A)=0.01$%$=0.0001$
$P(A^c)=1-0.0001=0.9999$
$P(B|A)=99.9$%$=0.999$
$P(B|A^c)=100$%$-99.99$%$=0.01$%$=0.0001$
$P(B)=P(B|A)P(A)+P(B|A^c)P(A^c)=0.999\times0.0001+0.0001\times0.9999=0.00019989$
$P(B)=0.019989\%\approx 0.02\%$
