Consider a large program consisting of N individual components that can freely interact with each other. Suppose each component has a probability p of being right. Then the probability P that the whole program is right satisfies the following inequality:
P <= pN.
On the one hand, we would like N to be very large, so that we can exploit the immense computer power that is available to us. On the other hand, we want P to approximate 1, because we want the overall program to be correct.
The implication is that each component has to be designed with a confidence level p close to 1 as well! This shows that reliability becomes a key issue for each and every component.
→ See EWD303 for Dijkstra's original explanation.