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Unit 8

Multi-step Experiments

Probability and Sampling

Lesson 9

Expressions and Equations

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Let’s look at probabilities of experiments that have multiple steps.

Unit 8 ● Lesson 9

Learning

Goal

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True or False?

Unit 8 ● Lesson 9 ● Activity 1

Is each equation true or false? Explain your reasoning.

8 = (8 + 8 + 8 + 8) ÷ 3

(10 + 10 + 10 + 10 + 10) ÷ 5 = 10

(6 + 4 + 6 + 4 + 6 + 4) ÷ 6 = 5

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Warm-up

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

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Spinning a Color and Number

Unit 8 ● Lesson 9 ● Activity 2

What do you notice? What do you wonder?

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Notice and Wonder

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

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Spinning a Color and Number

Unit 8 ● Lesson 9 ● Activity 2

The other day, you wrote the sample space for spinning each of these spinners once.

What is the probability of getting:

  • Green and 3?
  • Blue and any odd number?
  • Any color other than red and any number other than 2?

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

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Spinning a Color and Number

Unit 8 ● Lesson 9 ● Activity 2

  • How did you calculate the number of outcomes in the sample space?
  • Although we had the sample space for this situation in a previous problem, how could you find the sample space if you did not know it already?
  • For each problem, how many outcomes were in the event that was described? How did you count them?

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

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Cubes and Coins

Unit 8 ● Lesson 9 ● Activity 3

The other day you looked at a list, a table, and a tree that showed the sample space for rolling a number cube and flipping a coin.

  • Your teacher will assign you one of these three structures to use to answer these questions. Be prepared to explain your reasoning.
    • What is the probability of getting tails and a 6?
    • What is the probability of getting heads and an odd number?

Pause here so your teacher can review your work.

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

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Cubes and Coins

Unit 8 ● Lesson 9 ● Activity 3

  • Suppose you roll two number cubes. What is the probability of getting:
    • Both cubes showing the same number?
    • Exactly one cube showing an even number?
    • At least one cube showing an even number?
    • Two values that have a sum of 8?
    • Two values that have a sum of 13?
  • Jada flips three quarters. What is the probability that all three will land showing the same side?

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

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Cubes and Coins

Unit 8 ● Lesson 9 ● Activity 3

  • Which representation did you use for each of the problems?
  • Do you think you will always try to use the same representation, or can you think of situations when one representation might be better than another?
  • Did you have a method for finding the number of outcomes in the sample space or event that was more efficient than just counting them?
  • One of the events had a probability of zero. What does this mean?
  • What would be the probability of an event that was certain?
  • Jada was concerned with having all the coins show the same side. What would be the probability of having at least 1 coin not match the others?
  • How do the answers to Jada’s question and the one we just answered relate to one another?

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

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Pick a Card

Unit 8 ● Lesson 9 ● Activity 4

Imagine there are 5 cards. They are colored red, yellow, green, white, and black. You mix up the cards and select one of them without looking. Then, without putting that card back, you mix up the remaining cards and select another one.

  • Write the sample space and tell how many possible outcomes there are.
  • What structure did you use to write all of the outcomes (list, table, tree, something else)? Explain why you chose that structure.
  • What is the probability that:
    • You get a white card and a red card (in either order)?
    • You get a black card (either time)?
    • You do not get a black card (either time)?
    • You get a blue card?
    • You get 2 cards of the same color?
    • You get 2 cards of different colors?

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

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Pick a Card

Unit 8 ● Lesson 9 ● Activity 4

  • What would change about your calculations if the experiment required replacing the first card before picking a second card?
  • What do you notice about the sum of the probability of getting a black card and the probability of not getting a black card?
  • Explain why these outcomes might have probabilities with this relationship.

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

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Multi-step Experiments

Unit 8 ● Lesson 9

  • When the outcomes in the sample space are equally likely, how is the size of the sample space used to calculate the probability of an event?
  • Now that you’ve have plenty of practice, do you have a favorite method for writing out the sample space?
  • Are there times that one strategy for writing out the sample space makes more sense than others?

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Lesson Synthesis

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

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Unit 8 ● Lesson 9

I can use the sample space to calculate the probability of an event in a multi-step experiment.

Learning

Targets

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A Number Cube and 10 Cards

Unit 8 ● Lesson 9 ● Activity 4

Lin plays a game that involves a standard number cube and a deck of ten cards numbered 1 through 10. If both the cube and card have the same number, Lin gets another turn. Otherwise, play continues with the next player.

What is the probability that Lin gets another turn?

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Cool-down

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

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This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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