1 of 14

Unit 8

Estimating Probabilities Through Repeated Experiments

Probability and Sampling

Lesson 4

Expressions and Equations

​

​

7

2 of 14

Let’s do some experimenting.

Unit 8 ● Lesson 4

Learning

Goal

7

3 of 14

Decimals on the Number Line

Unit 8 ● Lesson 4 ● Activity 1

  1. Locate and label these numbers on the number line.
    1. 0.5
    2. 0.75
    3. 0.33
    4. 0.67
    5. 0.25
  2. Choose one of the numbers from the previous question. Describe a game in which that number represents your probability of winning.

7

Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

4 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

5 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

Mai plays a game in which she only wins if she rolls a 1 or a 2 with a standard number cube.

  1. List the outcomes in the sample space for rolling the number cube.�
  2. What is the probability Mai will win the game? Explain your reasoning.�
  3. If Mai is given the option to flip a coin and win if it comes up heads, is that a better option for her to win?�
  4. With your group, follow these instructions 10 times to create the graph.
  5. One person rolls the number cube. Everyone records the outcome.
  6. Calculate the fraction of rolls that are a win for Mai so far. Approximate the fraction with a decimal value rounded to the hundredths place. Record both the fraction and the decimal in the last column of the table.
  7. On the graph, plot the number of rolls and the fraction that were wins.
  8. Pass the number cube to the next person in the group.

​

​

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

6 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

  1. What appears to be happening with the points on the graph?
  2. a. After 10 rolls, what fraction of � the total rolls were a win?
    1. How close is this fraction to the probability that Mai will win?

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

7 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

  1. Roll the number cube 10 more times. Record your results in this table and on the graph from earlier.

​

​

​

​

​

​

​

​

  • a. After 20 rolls, what fraction of the total rolls were a win?
    1. How close is this fraction to the probability that Mai will win?

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

8 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

9 of 14

In the Long Run

Unit 8 ● Lesson 4 ● Activity 2

  • How many times did the entire class roll the number cubes?
  • Based on the probability predicted in the second question, how many times do we expect the class to have simulated a win for Mai? How does this compare to the actual number of wins the class rolled?

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

10 of 14

Due For a Win

Unit 8 ● Lesson 4 ● Activity 3

  1. For each situation, do you think the result is surprising or not? Is it possible? Be prepared to explain your reasoning.
    1. You flip the coin once, and it lands heads up.�
    2. You flip the coin twice, and it lands heads up both times.�
    3. You flip the coin 100 times, and it lands heads up all 100 times.

�

  • If you flip the coin 100 times, how many times would you expect the coin to land heads up? Explain your reasoning.�

​

7

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

11 of 14

Estimating Probabilities Through Repeated Experiments

Unit 8 ● Lesson 4

  • You conduct a chance experiment many times and record the outcomes. How are these outcomes related to the probability of a certain event occurring?
  • What is the probability of rolling a 2, 3, or 4 on a standard number cube? If you roll 3 times and none of them result in a 2, 3, or 4, does the probability of getting one of those values change with the next roll?
  • The probability of getting the flu during flu season is . If a family has 8 people living in the same house, is it guaranteed that one of them will get the flu? If a country has 8 million people, about how many do you expect will get the flu? Does this number have to be exact?

7

Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

12 of 14

Unit 8 ● Lesson 4

  • I can estimate the probability of an event based on the results from repeating an experiment.
  • I can explain whether certain results from repeated experiments would be surprising or not.

Learning

Targets

7

13 of 14

Fiction or Non-fiction?

Unit 8 ● Lesson 4 ● Activity 4

A librarian is curious about the habits of the library's patrons. He records the type of item that the first 10 patrons check out from the library.

Based on the information from these patrons . . .

  1. Estimate the probability that the next patron will check out a fiction book. Explain your reasoning.
  2. Estimate the number of DVDs that will be checked out for every 100 patrons. Explain your reasoning.

7

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

14 of 14

Lesson Video

SLIDESMANIA.COM