Answer
$\frac{19}{1044}$
Work Step by Step
We know that $probability=\frac{\text{number of favorable outcomes}}{\text{number of all outcomes}}$
The number of all outcomes is $(9+11+1+124)(9+11+1+124-1)=145\cdot144=20880$, because the first person can be anyone, the second can be anyone apart from the first one.
The number of good outcomes is $(9+11)(9+11-1)=20\cdot19=380$ because the first person has a positive screening test, the second also has a positive screening test but cannot be the first person.
Thus probability$=\frac{380}{20880}=\frac{19}{1044}$
