Unit 8

What Are Probabilities?

Probability and Sampling

Lesson 3

Expressions and Equations

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Let’s find out what's possible.

Unit 8 ● Lesson 3

Learning

Goal

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Which Game Would You Choose?

Unit 8 ● Lesson 3 ● Activity 1

Which game would you choose to play? Explain your reasoning.

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Game 1: You flip a coin and win if it lands showing heads.

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Game 2: You roll a standard number cube and win if it lands showing a number that is divisible by 3.

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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.

What’s Possible?

Unit 8 ● Lesson 3 ● Activity 2

Before this activity, let’s discuss the meaning of:

• random
• outcome
• sample space

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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.

What’s Possible?

Unit 8 ● Lesson 3 ● Activity 2

1. For each situation, list the sample space and tell how many outcomes there are.
1. Han rolls a standard number cube once.
2. Clare spins this spinner once.

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• Kiran selects a letter at random from the word “MATH.”
• Mai selects a letter at random from the alphabet.
• Noah picks a card at random from a stack that has cards numbered 5 through 20.

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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.

What’s Possible?

Unit 8 ● Lesson 3 ● Activity 2

• Next, compare the likelihood of these outcomes. Be prepared to explain your reasoning.
• Is Clare more likely to have the spinner �stop on the red or blue section?

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• Is Kiran or Mai more likely to get the letter T?
• Is Han or Noah more likely to get a number that is greater than 5?
• Suppose you have a spinner that is evenly divided showing all the days of the week. You also have a bag of papers that list the months of the year. Are you more likely to spin the current day of the week or pull out the paper with the current month?

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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.

What’s Possible?

Unit 8 ● Lesson 3 ● Activity 2

• A standard number cube is rolled. What is the sample space?
• How many outcomes are in the sample space?
• What is the probability of rolling a 3? Explain your reasoning.
• An experiment has one of each different possible outcome. The probability of getting one of the outcomes is . How many outcomes are in the sample space?

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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.

What’s in the Bag?

Unit 8 ● Lesson 3 ● Activity 3

Your teacher will give your group a bag of paper slips with something printed on them. Repeat these steps until everyone in your group has had a turn.

• As a group, guess what is printed on the papers in the bag and record your guess in the table.
• Without looking in the bag, one person takes out one of the papers and shows it to the group.
• Everyone in the group records what is printed on the paper.

• The person who took out the paper puts it back into the bag, shakes the bag to mix up the papers, and passes the bag to the next person in the group.

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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.

What’s in the Bag?

Unit 8 ● Lesson 3 ● Activity 3

1. How was guessing the sample space the fourth time different from the first?
2. What could you do to get a better guess of the sample space?
3. Look at all the papers in the bag. Were any of your guesses correct?
4. Are all of the possible outcomes equally likely? Explain.
5. Use the sample space to determine the probability that a fifth person would get the same outcome as person 1.

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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.

What’s in the Bag?

Unit 8 ● Lesson 3 ● Activity 3

• After the first paper is drawn, a group guesses, 'A bunch of letter Cs.' What might they have picked on their first paper that would lead to that guess? What could that group get on their second paper that would make them change their guess? Could they get something for the second paper that would make them sure their guess was right?
• After the second paper is drawn, a group guesses, 'All of the consonants.' What might they have picked in their first two papers that would lead to that guess? What could that group get on their third paper that would make them change their guess? Could they get something that would make them more sure of their guess?
• How did you refine your predictions with each round?
• If you had a new bag of papers and you took out papers 50 times and never got a 'Z,' would that mean there is no 'Z' in the bag?

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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.

What Are Probabilities?

Unit 8 ● Lesson 3

• If you choose one letter at random from the English alphabet, how many outcomes are in the sample space? How many outcomes are in the event that a vowel (not including Y) is chosen?U.)
• What is the sample space of a chance experiment? How is the number of outcomes in the sample space related to the probability of an event if the outcomes in the sample space are equally likely?
• When there are 100 different outcomes in the sample space that are equally likely, what is the probability that a specific outcome will happen?

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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.

Unit 8 ● Lesson 3

• I can use the sample space to calculate the probability of an event when all outcomes are equally likely.
• I can write out the sample space for a simple chance experiment.

Learning

Targets

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Letter of the Day

Unit 8 ● Lesson 3 ● Activity 4

A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M.

1. What letters are possible to teach using this method? (Hint: There are 15.)
2. What are 4 letters that can't be taught using this method?
3. On TUESDAY, the mother writes the word on a piece of paper and cuts it up so that each letter is on a separate piece of paper. She mixes up the papers and picks one. What is the probability that she will choose the piece of paper with the letter Y? Explain your reasoning.

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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.

Word:

Random

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Definition:

Outcomes of a chance experiment are random if they are all equally likely to happen.

Example:

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Examples of random outcomes are:

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Word:

Sample Space

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Definition:

The sample space is the list of every possible outcome for a chance experiment.

Example:

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For example, the sample space for tossing two coins is:�

Heads - Heads

Heads - Tails

Tails - Heads

Tails - Tails

Lesson Video

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