ABSTRACT
This chapter introduces the main tools for computing simple probability problems which have a finite, discrete sample space, and to begin the development of uniform methods of solution as well as the development of the intuition. It shows a connection to the frequency approach to probability. The chapter develops in a more systematic way, the mathematical tools needed for finite sample spaces. There is a deliberate separation between the model of probability being assumed, the concepts needed for solving problems in that area, and the mathematical tools needed for their solution. The chapter also develops the mathematical concepts needed to proceed, such as permutations and combinations, the binomial distribution, random variables, the mean and variance, generating functions and convolutions. It shows the two concepts of probability, one based on symmetry and the other on the frequency of occurence, are not equivalent, that for the law to apply the variance must exist.
