## Probability and Odds

### Johnny WolfeSanta Rosa District Schools

#### Description

Students determine the probability and odds for various events.

#### Objectives

Interprets data that has been collected, organized, and displayed in charts, tables, plots.

Determines the probability for simple and compound events as well as independent and dependent events.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Probability and Odds (See Associated File)
- Probability and Odds Examples (See Associated File)
- Probability and Odds Worksheet (See Associated File)
- Probability and Odds Checklist (See Associated File)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Probability and Odds Examples. (See Associated File)
2. Have marking pens (for overhead).
3. Have Probability and Odds Examples (See Associated File) prepared and ready to demonstrate to students.
4. Have enough copies of Probability and Odds Worksheet (See Associated File) for each student.
5. Have enough copies of Probability and Odds Checklist (See Associated File) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, area, distributive property, and multiplying binomials.
NOTE: This lesson does not address compound events or dependent events. This lesson also does not address plots.

1. To help students understand the concept of probability, ask questions that require students to make educated guesses based on prior knowledge. (See #1 on Probability and Odds Examples) Answer student questions and comments.

2. Ask the students to come up with a definition of “probability;” you may have to help students put their thoughts into words. Many students have an idea of what “probability” is but have difficulty describing it. (See #2 on Probability and Odds Examples)

3. To test students' understanding of “probability,” probe their minds by giving them a situation where they must make a judgment based on “probability.” (See #3 on Probability and Odds Examples)

4. Ask students to name several areas in their lives that would involve probability. (See #4 on Probability and Odds Examples)

5. Work #5 Example. (See Probability and Odds Examples) Answer student questions and comments.

6. Work #6 Example. (See Probability and Odds Examples) Answer student questions and comments.

7. Work #7 Example. (See Probability and Odds Examples) Answer student questions and comments.

8. Work #8 Example. (See Probability and Odds Examples) Answer student questions and comments.

9. Discuss with the students what a “probability” of “zero” and “one” suggest. Also, introduce students to the idea that probability must lie in the range “0 <= P(event) <= 1.” (See #9 on Probability and Odds Examples)

10. Give the students an example that uses the terms “probability” and “odds.” Ask the students to describe the differences between “probability” and “odds.” Help the students come up with a definition of “odds.” Make sure students understand that the probability of the successes plus the probability of the failures must equal 1. (See #10 on Probability and Odds Examples)

11. Work #11 Example. (See Probability and Odds Examples) Answer student questions and comments.

12. Work #12 Example. (See Probability and Odds Examples) Answer student questions and comments.

13. Work #13 Example. (See Probability and Odds Examples) Answer student questions and comments.

14. Work #14 Example. (See Probability and Odds Examples) Answer student questions and comments.

15. Distribute the Probability and Odds Worksheet. (See Associated File)

16. Distribute the Probability and Odds Checklist. (See Associated File) Describe what constitutes an A, B, C, D, and F in the Checklist.

17. The students write their responses on the worksheets.

18. The teacher moves from student to student, observing the students' work and lending assistance.

#### Assessments

The student worksheet is collected and scored according to the Probability and Odds Checklist. (See Associated File)

#### Extensions

Have students collect data from a school sporting event such as football--i.e., how many times the ball was run/passed, the types of plays that were executed on 1st, 2nd, 3rd, and 4th downs. Then give the students a play situation and have them (based on their data) predict (probability and odds) what type of play the coach would have called.