12.1 The Counting Principle

1. 12.1 The Counting Principle Listing possibilites Fundamental Counting Principle Examples

2. Chapter goals In the 1st portion of this chapter, we focus on combinatorics – the branch of mathematics that deals with counting the number of possibilities / choices In the 2nd portion, we deal with probability Much of the vocabulary is similar for both topics There is a 3rd portion of the chapter (statistics) which we will skip

3. Terminology / Definitions A trial is an action such as flipping a coin, choosing a letter, or asking someone a survey question An outcome is the result of a single trial For example, the trial of flipping a coin has two outcomes (head or tail) The set of all possible outcomes is called the sample space An event consists of one or more outcomes of a trial For example if you roll a die, the event of rolling an even number consists of three outcomes (2, 4, or 6) Events are independent of each other if the choices for one event do NOT effect the choices for the other event

4. Listing the possibilities To list all outcomes in the sample space, consider making a tree diagram or a table (grid) This will allow you to systematically list possibilities without accidentally skipping any See example on the next slide

5. Example 1-1a