1. Unit 4: Probability Day 1: Counting Principles

2. Standards and Benchmarks 9.4.3.1 Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities.

3. Learning Targets a) I can apply multiplication principles to determine the number of possible outcomes in a sample space. b) I can apply the addition principle to determine the number of possible outcomes in a sample space. c) I can apply tree diagrams to determine the number of possible outcomes in a sample space. d) I can calculate the probability of an event.

4. Counting Principles Exploration: Read through The following and discuss possible solutions with a partner

6. Counting Principles Using the exploration results, you have just discovered the Fundamental Counting Principle which is a method for determining the number of ways choices can be made when given multiple options.

7. Counting Principles A password for a site consists of 4 digits followed by 2 letters. The letters A and Z are not used, and each digit or letter many be used more than once. How many unique passwords are possible? A “make-your-own-adventure” story lets you choose 6 starting points, gives 4 plot choices, and then has 5 possible endings. How many adventures are there?

8. Counting Principles Sometimes when trying to count the number of ways an event can happen there may be other details to pay attention to that imply order is important or order isn’t important. This is based upon being a permutation or a combination.

9. Counting Principles

12. Read these over with a partner and decide whether it is a permutation or combination

13. Counting Principles Group time: WKST Practice 1 (11-1 Practice B) Individual work time: WKST: Practice 2 (10-8 Practice B) WKST: Problem Solving

14. Counting Principles – Exit Quiz 1. Six different books will be displayed in the library window. How many different arrangements are there? 2. The code for a lock consists of 5 digits. The last number cannot be 0 or 1. How many different codes are possible? 3. The three best essays in a contest will receive gold, silver, and bronze stars. There are 10 essays. In how many ways can the prizes be awarded? 4. In a talent show, the top 3 performers of 15 will advance to the next round. In how many ways can this be done?