These are fairly extreme examples but point out the importance of sensitivity, specificity and prevalence of disease. However you have to do the best you can even with extreme examples, (Medicine always has to deal with uncertainty and probability rather than always be sure). With really rare diseases the test has to have really high specificity (99.99%) if you want to be able to rely upon a positive test and not have to retest one way or another a whole lot of people who turn out to be false positives, (HIV negative people testing positive would not be at all happy). The sensitivity is important if you want to be reassured by a negative test, especially when a condition is common.