This lecture will give some simple examples of the use of the probabilistic method. It uses tools from probability to prove the existence of combinatorial objects that can be hard to find deterministically. This idea was pioneered by the great Hungarian mathematician Paul Erdos and it is now part of the standard toolkit for combinatorialists. We will consider four problems where we can obtain results very easily via random methods. On the other hand, in these instances, non-random constructions seem much harder to obtain.