6.1: Definitions and Basic Counting
Read from the Introduction to Probability through Section 1.2. This reading motivates our study of probability and also counting - because counting often comes up in the analysis of problems that we solve using probability.
6.1.1: What Is a Sample Space?
Read Section 1.3 on pages 3 - 5. The previous reading introduced a four-step process for building a probabilistic model to analyze and solve problems using probability. This reading discusses the first step.
6.1.2: What Is an Event?
Read Section 1.4 on pages 5 - 6. This reading discusses the second step of the four-step process for building a probabilistic model for solving probability problems.
6.1.3: Equally Likely Probability Formula
Read Section 1.5 and Section 1.6 on pages 6 - 9. This reading discusses the third and fourth steps of the four-step process for building a probabilistic model for solving probability problems. In the third step, probabilities are assigned using the possibility tree drawn during steps one and two. In step three, probabilities are assigned to the edges of the tree. At each level of the tree, the branches of a node represent possible outcomes for that node. If the outcomes of a node are assigned the same probability (the outcomes of a node add to 1), we say that they represent equally likely outcomes.
6.1.4: Counting Elements of Lists and Sublists
Read through Section 1.4. This work presents some strategies and rules that aid us in counting members of sets arising in the analysis of probability problems.
Section 1.3 illustrates the bijection rule for arrays and lists. The bijection rule can be applied to counting the elements of an array. The elements of a list can be mapped via a bijection to a one-dimensional array. Thus, because we can count the elements of a list, we can count the elements of such an array. (We count the elements of a list, by walking down the list and incrementing a tally, initialized to zero, by one for each item of the list.)