3.1 Designing Another Spinner

Focus Question:
How can we use a probability simulation to make predictions?

Part 1: Looking At Spinners

Part 2: Analyzing a Spinner

Kalvin decides to use the spinner shown below:

1. What is the theoretical probability that the spinner will land on each time?
2. Based on the theoretical probabilities, if Kalvin spins the spinner 64 times, about how many times can he expect to go to bed at each time? Explain. Why do you think I chose 64 times?

Part 3: Testing the Spinner

1. Go to the following website: Spinner Site (you will probably need to use Firefox or Safari)
2. Click on "Change Spinner"
3. Design your spinner.
4. What was the experimental probability that the spinner landed on each time?
5. How many times did you "spin" the spinner? How did you decide that you had enough trials?
6. How do your experimental results compare to your theoretical probabilities?

Part 4: Designing a New Spinner

Pretend that you are Kalvin's father.  Design a new spinner where it is "most likely" that Kalvin will go to bed at 9:00. Your spinner must have at least three different times and four different sections.

1. Test your spinner to be sure that it meets the criteria.
2. Take a screen shot and post it on your blog along with the theoretical probability of Kalvin going to bed at each time.

Scratching Spots:

• How might we design a simulation to test the probability of winning this contest?
• Try to use one of the probability tools to design a simulation for this situation. Be prepared to share your idea with others.

1. Based on your simulation, what is the experimental probability of winning this game?
2. Build a sample space to try and determine the theoretical probability of winning this game?
3. Is it worth it to spend $1000 at Tawanda's Toys to try and win video games?  Explain.

Homework:

• Design a Spinner Challenge Task
• ACE (13,14)
  
  
• Complete these Khan Academy activities:
  
  Probability Space
  Probability 1

Analyzing Compound Events

Focus Questions:

• How can you decide if a game is fair or not?
• How can we determine the theoretical probability of a compound event?

New Vocabulary:

• Fair Game - a game where the winning and losing are "equally likely"
• Sample Space - a list of all of the possible outcomes for an event.
• Tree Diagram - One type of "sample space" that is useful for events that have more than two parts.
• Compound Event - An event that has two or more parts or actions

Part 1: The Coin Game

Here are the rules of this game:

• You will toss three coins.
• If all three of the coins match, you get a point (and some money).
• If all three of the coins do NOT match, I get a point.
• Everybody gets one turn.
• At the end, the team (students or teacher) with the most points wins.

Part 2: Analzying the Game

1. What is the "experimental probability" of having all three coins match?
2. How many outcomes are there in this game?
3. Draw a sample space to determine all of the outcomes. (which type of sample space should you draw?)
4. Is this a "fair game"? Explain why or why not.

Part 3: The Bonus Prize

You are a contestant on Gee Whiz Everybody Wins and have made it to the final "Bonus Round".  In the Bonus Round you get to choose one of two games to play.

Game #1

• How to Play - Choose a block from Bag #1 THEN Choose from Bag #2
• How to Win - If you correctly predict the color of block that you will choose from each bag, you win.

Game #2

• How to Play - Choose a block from Bag #1 AND Bag #2 at the same time.
• How to Win - If you correctly predict the color combination that you will choose, you win.

Which game should you play?  Justify your decision with experimental and theoretical probabilities.

Part 4: Playing The Game

Task A:

• Run each experiment 18 times.  Record the results in your table.  Please remember to treat the bags kindly as they need to be used in multiple classes.
• After you have completed your experiment, fill out the forms below to contribute to class data.
• Game #1
• Game #2
• Here are the results from our class data: 

Part 5: Analyzing the Experiment

Answer the following questions in your squarebook:

1. What is the "experimental probability" of choosing each outcome for Game #1? Game #2?
2. What is the "theoretical probability" of choosing each outcome for Game #1? Game #2?
3. Are all of the outcomes "equally likely" for Game #1? Game #2?
4. How do the "experimental probabilities" and the"theoretical probabilities" compare for Game #1? Game #2?
5. Which Game should you choose to play? What should you predict if you play this game?

By the end of this lesson, you should be able to do the following:

• Determine whether a game is "fair".
• Describe how a "compound event" is different from a "simple event"
• Determine the "sample space" for a compound event using a probability tool such as a tree diagram or table

Homework:

1. ACE (9,11,12) (26) (*38)
2. Mid-Unit Summative on Investigations 1 and 2 next class.

Choosing Marbles

Focus Question: 

How do we determine the theoretical probability of some slightly more complex situations.

New Vocabulary:

• AND - All conditions described must be met.
• OR - Only one of the conditions described need to be met.
• NOT - The conditions listed must NOT occur.

Part 1: More Kalvin

For this part of the lesson you are going to do a quick formative assessment to see how well you understand the main focus questions from last week's lessons on probability.

You will do the assessment independently and can use calculators if you think that you need them.

Part 2: Simple Events

In this part of the lesson you will watch a video describing some of the basics around finding the theoretical probability of an outcome for a given event.  We have already talked about this a little bit, so this should be mostly a reinforcement of prior knowledge.

When you have finished watching the video, make sure that you complete the "On Your Own" questions.  Show your teacher when you have finished the questions.

Part 3: Choosing Marbles - Determining Theoretical Probabilities

The main part of this lesson is for you to now practice applying the concept of theoretical probability.  This is also in your textbook on page 30.

By the end of this problem you should be able to do the following:

• Determine the theoretical probability for a series of outcomes that contain the "OR", "AND", and "NOT" conditions.
• Develop a probability situation based on theoretical probabilities.

Homework:

1. ACE (p. 36) (6-7) (18-25)

Choosing Cereal

Focus Questions: 

• How does collecting more data helps you to predict the outcome of a probability situation?
• How can we use the results of a probability experiment to determine the "relative frequency" of an outcome?
• How does running a probability experiment help you determine how many possible outcomes there are as well as the likelihood of each outcome?

Kalvin would prefer to eat Cocoa Blast cereal for breakfast everyday.  His parents would prefer that he eats Health Nut Flakes.  In order to decide, his mother allows Kalvin to design a probability experiment.

Option 1: Flipping Coins

Kalvin will flip a coin.  If the results are heads, he will eat Cocoa Blast.  If the results are tails, he will eat Health Nut Flakes.

1. To run this experiment we will use our integer counters.  With your partner, designate one color to be "Heads" and the other color to be "Tails".  Make a note of your legend at the top of the table.
2. After you have completed your experiment, fill out this online form to contribute your data to our class data.
3. Here are the class results:
   
   
   RED = HEADS and BLUE = TAILS

Option 2: Tossing Cups

Kalvin will toss a cup.  If the cup lands on either end, he will eat Cocoa Blast.  If the cup lands on its side, he will eat Health Nut Flakes.

• Run your experiment 20 times.  Record the results in your table.  Please remember to treat the cups kindly as they need to be used in multiple classes.
• After you have completed your experiment, fill out this online form to contribute to the class data.  Here are the results of the class data:

Option 3: Matching Coins

Kalvin will toss two coins.  If the coins match, he will eat Cocoa Blast.  If the coins do NOT match he will eat Health Nut Flakes.

1. Run your experiment 30 times.  Record the results in your table.  Remember to use the "shake and drop" strategy.  
2. After you have completed your experiment, fill out this online form to contribute to the class data.  Here are the results of the class data:

At the end of this Problem you should be able to do the following:

• Describe how the accuracy of a probability experiment is influenced by the amount of data collected.
• Describe the difference between the probability of each outcome for an event and the relative frequency of each outcome for a probability experiment.
• Use the results of a probability experiment in order to predict the likelihood of each outcome.
• Extend the results of a probability experiment in order to predict the results of a similar probability experiment.

Here is what you MUST do before next class:

• Complete all of the questions on the handout.
• ACE (3, 6, 8, 10)
• Khan Academy: Simple Probability and Experimental Probability

Introduction to Probability - Block G

Our next unit is my personal favorite - Probability.  This is a unit where we get to explore "how likely" is something to happen.  This is a great skill to have in anybody's decision making skill set.

First of all, let's start by playing a game.  The rules are very simple:

• Predict what you will pick out of the bag.
• If you are correct, you win
• Questions???

Next, let's get a sense of what you will be doing in this unit.  Take a look at the "I Can..." statements.  On the scale above each statement, place a mark to indicate how well you think you can do each of the unit objectives.  Remember that this is the beginning of the unit so I am not expecting you to be an expert.

Now...let's get some basic probability language down.  Take a look at this video and complete the note-taking sheet that you have been provided with.

Here are some key words that you should be able to use next class:

• Event
• Outcome
• Certain
• Impossible
• Likely
• Unlikely
• Theoretical Probability
• Experimental Probability

What does it mean if outcomes are "Equally Likely"?

If two or more outcomes are "equally likely", it means that they have an equal chance of occurring.  Think about the game we just played.  Each block had an equally likely chance of being picked, but that didn't necessarily mean that each color had an "equally likely" chance of being picked.

Take a look at the spinners below and see if you can decide which one has "equally likely" outcomes.  Be prepared to justify your answer:

 

Now let's look at a variety of other events.  For each event, list all of the possible outcomes (if this hasn't already been done for you) and then decide whether the outcomes are all "equally likely" to occur.

As you can see, this can get a little bit tricky.

Now let's Practice

I have included a link to a Khan Academy activity that addresses the same things that are discussed in the video above.  You need to complete this before next class: Understanding Probability

Before next class you MUST have completed the following:

• Self assess your current level of understanding of each "I can..." statement
• Watch the "What is Probability" video and complete the note-taker page.
• Pass the first level of the "Understanding Probability" exercise on Khan Academy
• ACE (11-18) p. 19
• ACE (26-29) p. 23

Introduction to Probability - Block C and E

Our next unit is my personal favorite - Probability.  This is a unit where we get to explore "how likely" is something to happen.  This is a great skill to have in anybody's decision making skill set.

First of all, let's get a sense of what you will be doing in this unit.  Take a look at the "I Can..." statements.  On the scale above each statement, place a mark to indicate how well you think you can do each of the unit objectives.  Remember that this is the beginning of the unit so I am not expecting you to be an expert.

Now...let's get some basic probability language down.  Take a look at this video and complete the note-taking sheet that you have been provided with.

Here are some key words that you should be able to use next class:

• Event
• Outcome
• Certain
• Impossible
• Likely
• Unlikely
• Theoretical Probability
• Experimental Probability

Now let's Practice

I have included a link to a Khan Academy activity that addresses the same things that are discussed in the video above.  You need to complete this before next class: Understanding Probability

Before next class you MUST have completed the following:

• Self assess your current level of understanding of each "I can..." statement
• Watch the "What is Probability" video and complete the note-taker page.
• Pass the first level of the "Understanding Probability" video on Khan Academy