There are many students who have been introduced to the subject of probability in elementary courses in such a way as to encourage the notion that probability is highly intuitive and not very precise from a mathematical standpoint. Working problems in probability often becomes little more than out-guessing the teacher. It is hoped that this brief introduction will clarify the notions of probability, event, and sample space,  at least in the finite case. The finite case is sufficiently general to solve many problems arising in situations familiar to the student. For other cases and more involved problems, the reader is referred to the more extensive treatments listed in the bibliography.