A positive result needs context

The question is retained before an explanation is adopted.

Invented arithmetic: 9 true positives and 99 false positives among 1,000 stones.

A rare target can produce fewer true positives than false positives, even when a test appears impressive.

What is the target frequency? What are the sensitivity and false-positive rate? What follows when all three are considered together?

The exciting stone is not the entire sample.

108 positive tests: 9 contain gold; 99 do not