Events are said to be independent when the outcome of one event does not affect the other.

On the other hand, two events are dependent when the occurrence or nonoccurrence of one event does affect the probability of the other event.

This is an important distinction, as we shall see.

When using the multiplication rule for independent events, sometimes we use the percent chance of success, other times we use the percent chance of failure. We must think about what we are trying to calculate when deciding which to use. If we want to calculate the probability that all the independent events will fail, then we would use the chances of failure. On the other hand, if we want the chance that all the independent events will succeed, then we use the chances of success. In a situation where we want the probability that one or more of the events will fail, then we would use one minus the multiplication of the chances of success (one minus the chance that all of the events will succeed will be the chance that one or more would fail).

Simple example: A software development project is going to proceed concurrently with the development of a new piece of hardware required to implement the software. Scheduled completion dates for both developments have been determined and a project plan has been created. Both projects can proceed independently until their respective completions (probably an unwarranted assumption, but I said this is a simple example!). Both projects must succeed in order for overall success to be achieved.