Probability measures the likeliness that a particular event will occur. When mathematicians (us, for now!) speak of an event, we are referring to a set of potential outcomes of an experiment, or trial, to which we can assign a probability of occurrence.
Probabilities are expressed as a number between 0 and 1 (or as a percentage out of 100). An event with a probability of 0 denotes an impossible outcome, and a probability of 1 describes an event that is certain to occur.
The canonical example of probability at work is a coin flip. In the coin flip event, there are two outcomes: the coin lands on heads or the coin lands on tails. Pretending that coins never land on their edge (they almost never do), those two outcomes are the only ones possible. The sample space (the set of all possible outcomes), therefore, is {heads, tails}. As the entire sample space is covered by these two outcomes, they are said to be collectively exhaustive.
The sum of the probabilities of collectively...