A Program of The Actuarial Foundation. Aligned with Common Core State and NCTM Standards.

What is an actuary? An actuary is an expert in statistics who works with businesses, governments, and organizations to help them plan for the future. Actuarial science is the discipline that applies math and statistical methods to assess risk.

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GRADE
6-8

DURATION
30

COLLECTION
The Power of Probability

# Lesson 2: Simple Probability and Sampling

STANDARDS (CCSS AND NCTM)

• Grade 7: Statistics and Probability (CCSS 7.SP.1 and 2)
• Grades 6–8: Reason Abstractly and Quantitatively, Construct Viable Arguments, Model with Mathematics, and Look for and Make Use of Structure (CCSS MP2-4, and 7)
• NCTM: Data Analysis and Probability

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

Click for whiteboard-ready printables.

DIRECTIONS

Introduction to Basic Probability and Sampling

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. Guided Practice: Individually or in pairs, ask students to calculate the following probabilities when rolling a six-sided die:

• Rolling a number more than four (2/6 or 1/3. 5 and 6 are the favorable outcomes)
• Rolling any number but 2 (5/6. 1, 3, 4, 5, and 6 are the favorable outcomes)

Also, ask students to evaluate the following statement: Janet said she was 110% sure she aced the last math test. For both problems, students should share answers and explain their thinking to the class.

5. Independent Practice: Distribute Worksheet 2 and calculators. Read the introduction and review the facts with the class. Ask students to complete the worksheet. Explain that the bonus question requires them to apply what they learned about probability in Lesson 1.

Check for Understanding: 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.

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