2. Notes Over 12 - 4 1. A school team sells caps in two colors (blue or white), two sizes (child or adult), and two fabrics (cotton or polyester). Draw a tree diagram to find the number of cap choices. blue white child adult child adult cotton polyester cotton polyester cotton polyester cotton polyester There are 8 possible cap choices. Counting Outcomes and Theoretical Probability

3. Notes Over 12 - 4 Counting Outcomes and Theoretical Probability If there are m ways of making one choice, and n ways of making a second choice, then there are m n ways of making the first choice followed by the second choice. Counting Principle

4. Notes Over 12 - 4 Counting Outcomes and Theoretical Probability Theoretical Probability

5. Notes Over 12 - 4 2. A freshman class sells cold drinks. Customers can choose small, medium, or large. There are five drinks: cola, diet cola, root beer, lemonade, and water. Customers can choose ice or no ice. Use the counting principle to find the total number of possibilities. Counting Outcomes and Theoretical Probability What is the theoretical probability that a customer will order a medium diet coke with no ice?

6. Notes Over 12 - 4 Counting Outcomes and Theoretical Probability 3. Draw a tree diagram to find the sample space for tossing two coins. Then find the probability of tossing two heads. heads tails heads tails heads tails There are 4 possible outcomes. Only one outcome is tossing two heads.

7. Notes Over 12 - 4 4. In some state lotteries, the winning number is made up of four digits chosen at random. Suppose a player buys two tickets with different numbers. What is the probability that the player has a winning ticket? (each digit can be a number from 0 to 9) Counting Outcomes and Theoretical Probability

8. Pg. 629 #1 – 3, 4 – 17 1. There are 3 ways of performing Task A. There are 4 ways of performing Task B. Use a tree diagram to find the number of ways there are to perform Task A and then Task B. 1 1 4 There are 12 possible ways. Counting Outcomes and Theoretical Probability 2 3 2 1 4 2 3 3 1 4 2 3

9. Pg. 629 #1 – 3, 4 – 17 2. There are 8 roads leading from Marsh to Taft and 7 roads leading from Taft to Polk. How many possible routes are there for driving from Marsh to through Polk? There are 56 possible ways. Counting Outcomes and Theoretical Probability

10. Pg. 629 #1 – 3, 4 – 17 3. Find the probability of rolling a 3 on each of two number cubes. There are 36 possible ways. Counting Outcomes and Theoretical Probability There is only one way of rolling a 3 on both of them.

11. Pg. 629 #1 – 3, 4 – 17 Counting Outcomes and Theoretical Probability