# Lesson 2: Simple Probability and Sampling

Using a six-sided die, students learn the difference between outcomes and events, as well as practice adding probabilities of outcomes to determine the probability of an event. Students will also experiment with using proportions to make predictions based on a sample.

**OBJECTIVE**

- Students will understand that proportions can be used to make predictions about a population based on a sample;
- Students will identify the difference between outcomes and events; and
- Students will add the probabilities of the outcomes that are part of an event to determine the probability of an event.

**MATERIALS**

- one six-sided die (for demonstration)
- calculators
- Worksheet 2 Printable (PDF): "A Call for Assistants"
- Resource: Answer Key (PDF)
- Resource: Mini-Poster
- Resource: Standards Alignment Chart (PDF)
- Bonus Activity: Online Probability Challenge

Click for *whiteboard-ready printables*.

**DIRECTIONS**

Getting Started

1. Show a single six-sided die to the class. Ask what the possible outcomes are. Record the outcomes on the board. Ask the class to calculate the probability of each outcome as a fraction (1/6 for each). Indicate that when the probabilities of all individual outcomes are added together, the sum is 1.

2. Ask what the probability of rolling an even number is. Students should indicate that the probability is 1/2 or 50%. They may calculate this by writing the number of favorable outcomes (3) over the total number of outcomes (6) to get 3/6, which should be reduced to lowest terms (1/2). Show how they could also determine this by adding the probability of each even outcome (1/6 + 1/6 + 1/6) to arrive at 3/6 or 1/2 or 50%.

3. Explain that the even outcomes here are 2, 4, or 6. Rolling an even number is called an event. The sum of the even outcomes equals the probability of an event. If necessary, repeat with other examples, such as the probability of rolling a number other than a 3, the probability of rolling a number less than 3, etc.

4. Distribute Worksheet 2 and calculators. Read the introduction and review the facts with the class.

5. Ask students to complete the worksheet. Explain that the bonus question requires them to apply what they learned about probability in Lesson 1. Review answers as a class. Make sure that the review includes a discussion of how proportions are used to make predictions about the population as a whole by using the results of a poll of a sample of the total customer base (e.g., 12/2,000 = x/50,000) and the validity of doing so. Worksheet Answer Key (PDF)

**LESSON EXTENSION**

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.