Plotting confidence against failure probability

This curve shows what can be predicted by randomly testing a piece of software with N tests. As N increases, the nose of the curve moves up and to the left, so that in the limit it rises immediately to 1 and remains there. This limit is the case of exhaustive testing when we have perfect confidence that the software cannot fail.

The intuitive form of the relationship is evidently correct. If a number of tests have been carried out successfully, this can be interpreted as high confidence that the possibility of failure is a little less than 1 (that is, we are pretty sure that the program doesn't fail all the time), at the upper right part of the graph; or, the same information can be interpreted as lower confidence that the program is quite unlikely to fail, near the origin of the graph. The confidence, and what we have confidence in, can be traded off for one another.