1. Chapter 12: Data Analysis & Probability 12.4 Counting Outcomes & Theoretical Probability

2. Tree Diagrams for Outcomes outcomes: possible events for a situation tree diagram: –starts with one set of events –lists the possibilities for each type of event –looks like a tree

3. Example 1 The NFL sells hats in two sizes, child and adult. Fans have a choice of hats for the top 10 teams that year. Hats can also come in black or white. How many choices of hats do fans have?

4. Counting Principle If there are m ways of making one choice, and n ways of making a second choice, then there is m · n ways of making the first choice followed by the second.

5. Example 2 How many ways can I choose a sandwich, if there’s three types of bread, four types of cheese, and five types of meat?

6. Theoretical Probability P(event) = number of favorable outcomes number of possible outcomes

7. Sample Space list of all possible outcomes tree diagrams are one way to show this

8. Example 3 Show the sample space for rolling a die three times.

9. Example 3a You roll the die three times. What is the probability that you roll a 3, then a 4, then a 5, in that order?

10. Example 4 I have a set of cards, labeled 1-10. Show the sample space for drawing a card, then replacing it. What is the probability that I draw a 2, then draw a 2 again?