 Consider a system that has a set of n events, where those events are mutually exclusive, which means one event is not a sub-event of another, or that those events occur independently. And those events that we have are exhaustive, which means in the system no other events can occur apart from those n that we know about. If for event i we know the expected value of that event, E i, and the probability of that event i occurring is P i, then the total expected value for the system is the sum across all events from i equal 1 to n of the expected value of each event times by the probability of each event.