The F-measure - the number of distinct test cases to detect the first program failure - is an effectiveness measure for debug testing strategies. We show that for random testing with replacement, the F-measure will be distributed according to the geometric distribution. A simulation study examines the distribution of two adaptive random testing methods, to study how closely their sampling distributions approximate the geometric distribution, revealing that in the worst case scenario, the sampling distribution for adaptive random testing is very similar to random testing. Our results have provided an answer to a conjecture that adaptive random testing is always a more effective alternative to random testing, with reference to the F-measure. We consider the implications of our findings for previous studies conducted in the area, and make recommendations to future studies.