The Law of Total Probability uses families of events that are both totally exhaustive and also mutually exclusive. This number is called the probability of the event. The purpose is to quantify the tendency, or propensity, or believability, of the event. From these three simple rules, a lot of interesting facts about probabilities are inevitable. There are a couple of mathematical complications.
Most mathematicians extend the second bullet to include infinite sums.
Also, for some sample spaces, mathematicians know how to construct probabilities that don't work for all the subsets. In other words, there are sometimes subsets that can't be events with probabilities. Your probabilities may depend on your personal decisions. For example, the probability that you will be stranded on the highway sometime within the next year may depend on what kind of transportation you choose to use throughout the year.