Today’s Materials

• pencil
• notebook
• glue

What Are

Probabilities?

Lesson 3

Let’s find out what’s possible!

Which Game Would You Choose?

Warm Up

Which game would you choose to play?

Explain your reasoning.

Game 1:

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

Game 2:

You roll a standard number cube and win if it lands showing a number divisible by 3.

What’s Possible?

Activity 1

random

doing something so that the outcomes are based on chance

Remember…

each possible results for a chance experiment is called an outcome

sample space

the set of all possible outcomes

Work for 10 minutes with your partner.

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Then we’ll talk as a class!

In this activity, all of the outcomes are equally likely within each sample space.

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Sometimes it is important to have an actual numerical value rather than a sense of likelihood.

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To answer how probable something is to happen, we assign a probability.

• Probabilities are values between 0 and 1 and can be expressed as a fraction, decimal, or percentage.
• Example: Something that has 50% chance of happening, like a coin landing heads up, or the probability is ½ or 0.5.

To answer how probable something is to happen, we assign a probability.

• When each outcome in the sample space is equally likely, we may calculate the probability of a desired event by dividing the number of outcomes that the event occurs by the total number of outcomes in the sample space.

desired outcomes�total outcomes

A standard number cube is rolled.

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What is the probability of rolling a 3? Explain.

1, 2, 3, 4, 5, 6

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How many outcomes are in the sample space?

6 outcomes

A standard number cube is rolled.

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What is the probability of rolling a 3? Explain.

⅙

there is a 3 and 6 outcomes �in the sample space

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An experiment has one of each different possible outcome. The probability of getting one of the outcomes is 1/30.

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How many outcomes are in the sample space?

“Are you ready for more?”

Are there any outcomes for two people in this activity that have the same likelihood?

Explain or show your reasoning.

What’s in the Bag?

Activity 2

Please copy the table into your notebook.

Your team will be given 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 in back in the bag, shakes it up, and passes the bag to the next teammate.

Discuss these questions as a team:

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.

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?

Today’s Goals

• 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.

If you choose one letter at random from the English alphabet, how many outcomes are in the sample space?

There are 26 outcomes in the sample space.

If you choose one letter at random from the English alphabet, how many outcomes are in the event that a vowel (not including Y) is chosen?

There are 5 outcomes that are vowels (A, E, I, O, U).

What is the sample space of a chance experiment?

the list of all possible outcomes for an 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 more outcomes in the sample space, the probability of a single outcome occurring is lower.

When there are 100 different outcomes in the sample space that are equally likely, what is the probability that a specific outcome will happen?

1/100 1% 0.01

Letter of the Day

Cool Down