Final answer:
The greatest triumph in a case-control study was the association found between past smoking behavior and current lung cancer status. However, it is not 100% provable due to the limitations of case-control studies in establishing causation.
Step-by-step explanation:
The greatest triumph in a case-control study was the discovery of a strong association between past smoking behavior and current lung cancer status. In the study conducted by Doll and Hill on 700 lung cancer patients and 700 people without lung cancer, they found that people who smoked were more likely to have lung cancer compared to those who did not smoke.
This finding is not 100% provable because case-control studies can only show an association between variables and cannot establish causation. While the study showed a strong association, it does not prove that smoking directly causes lung cancer as there may be other factors at play.