### Lesson Plan

# How to Use Compound Probability

In this lesson, students will use a tree diagram to derive the formula for compound probability, then use it to calculate the probability of multiple independent events.

Grades

6–8

### Objectives

**Students will:**

- Use a tree diagram to derive the formula for compound probability
- Use the formula for compound probability to calculate the probability of multiple independent events

### Materials

- One coin (for demonstration)
- The Power of Probability Worksheet: Math Masters printable
- Bonus Power of Probability Worksheet: Mind Your Own Business! printable

- Answer Key: The Power of Probability printable
- Standards Chart: The Power of Probability printable
**Optional:**Online Probability Challenge**Optional:**The Power of Probability Classroom Poster printable

- One coin (for demonstration)
- The Power of Probability Worksheet: Math Masters printable
- Bonus Power of Probability Worksheet: Mind Your Own Business! printable

- Answer Key: The Power of Probability printable
- Standards Chart: The Power of Probability printable
**Optional:**Online Probability Challenge**Optional:**The Power of Probability Classroom Poster printable

### Set Up

- Make a class set of The Power of Probability Worksheet: Math Masters printable and the Bonus Power of Probability Worksheet: Mind Your Own Business! printable.
- Print a copy of the Answer Key: The Power of Probability printable.
**Optional:**Hang a copy of The Power of Probability Classroom Poster printable in your classroom.

### Lesson Directions

**Introduction to Compound Probability**

**Step 1:** Show the coin to the class and ask what is the probability of the coin landing on heads.

**Step 2:** Recall the work done in the Make Sense of Basic Probability lesson plan on tree diagrams and ask for a volunteer to explain how all the outcomes for three flips in a row could be depicted.

**Step 3:** Ask what the probability of a coin landing on heads three times in a row would be. Walk the students through a tree diagram to demonstrate that there is one outcome for three heads in a row while there are seven unfavorable outcomes (HHT, HTT, HTH, TTT, TTH, THT, THH), so the probability is one out of eight or 1/8 or 12.5%.

**Step 4:** Ask if there is a way to calculate the probability of tossing three heads in a row without setting up the tree diagram. If necessary, point out that the probability of one heads flip is 1/2 or 50% or .5 and, for three heads in a row:

1/2 x 1/2 x 1/2 = 1/8 *or*

.5 x .5 x .5 = .125 *or*

50% (.5) x 50% (.5) x 50% (.5) = 12.5% or .125

### Guided Practice

**Step 5:** Individually or in pairs, ask students, using both the formula and a tree diagram, to determine:

- The probability of rain in both Chicago and San Francisco on the same day if the probability of rain is 20% in Chicago and 50% in San Francisco (20% x 50% = 10%)
- The probability of a six-sided die landing on an even number then flipping heads (50% x 50% = 25%)

Ask students to explain their answers to the class.

**Step 6: **Distribute Math Masters printable. Read the introduction and review the facts with the class. Ask students to complete the worksheet. Use your copy of the Answer key printable to review answers as a class. As a bonus activity, have students complete the Bonus Worksheet: Mind Your Own Business! printable.

### Lesson Extensions

Have students use the Online Probability Challenge to practice using probability skills for real-life purposes. This interactive online activity challenges students to use probability to help Rick and Athena plan a summer concert tour. This activity can be used as an in-class lesson activity or an out-of-the classroom extension.

### Standards

**Grade 7:**Statistics and Probability (CCSS**Grades 6–8:**Construct Viable Arguments & Model with Mathematics (CCSS**NCTM:**Data Analysis and Probability

For more information, download the comprehensive Standards Chart: The Power of Probability printable.