Part I: Introduction
Watch Bill Nye’s Probability Video: https://www.youtube.com/watch?v=Sqq4k50dxbI
1.
Define probability
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2. Place the following items on the probability scale below by placing the letter in the most
appropriate location:
a. You are going to school tomorrow
b. It is going to rain in Oak Park during the month of July
c. You are in math class right now
d. You are going to Hawaii after class
e. Write your own:_________________________________________________
f. Write your own:_________________________________________________
3. What does a probability near zero mean?
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What does a probability near 0.5 mean?
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What does a probability near 1.0 mean?
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Part II: Theoretical & Theoretical Probabilities
Class Discussion: Read the letter to the newspaper below. Think to yourself about the scenario. Be
prepared to share your thoughts and possible responses with the class.
Dear Carnival Carol,
There is a coin toss booth at the local fair. The game rules explain that you win if you toss
exactly 5 heads out of 10 total tosses. It seems like a person would win every single time since there
is a 50% probability of tossing a head each time. How is this booth still in business?
Sincerely,
Always a Winner
Watch video: https://www.youtube.com/watch?v=7m2fKiThesk
4. Define theoretical probability:
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5. Define experimental probability
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6. How does increasing the number of trials affect your experimental probability? For example,
how would your experimental probability change if conducting 10 experimental trials versus
100?
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7. Explain the difference between theoretical probability and experiential probability. Use the
example of flipping a coin 10 times.
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Part III: Probability Experiments
8. Coin Toss Probability:
Theoretical Probability of flipping a head.
Fraction: ____________
Decimal: ____________
Percent: ____________
Prediction: If you toss a coin 50 times, how times would it land on heads? _______
If you toss a coin 500 times? ________
Experiment: Use the following website’s coin flip simulator:
http://www.funmines.com/utilities/dice/
Experimental Results:
10 Flips: _____ # Heads
_____# of Tails
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
Experiment Results:
50 Flips: _____ # Heads
_____# of Tails
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
9. Dice Rolling Probability:
Theoretical Probability of rolling an even number on a 6-sided dice.
Fraction: ____________
Decimal: ____________
Percent: ____________
Prediction: If you roll a dice 50 times, how times would it land on an even number?
_______ If you roll it 500 times? ________
Experiment: Use the following website’s dice roll simulator:
http://www.funmines.com/utilities/dice/
Experimental Results:
10 Rolls: _____ # Even Numbered Rolls
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
Experimental Results:
50 Rolls: _____ # Even Numbered Rolls
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
10. Spinner Probability
Theoretical Probability of landing on red:
Fraction: ____________
Decimal: ____________
Percent: ____________
***HINT: All colors are not equally
likely to be spin.
Prediction: If you spin it 50 times, how times would it land on red? _______ If you
spin it 500 times? ________
Experiment: Place a paper clip in the center of the circle to use as a spinner.
Experimental Results:
10 Spins: _____ # Reds
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
Experimental Results:
50 Spins: _____ # Reds
Experimental Probability:
Fraction: ____________
Decimal: ____________
Percent: ____________
11. Complete the chart below using your data from above to compare the theoretical probabilities
to that of your experimental findings.
Coin
Dice
Spinner
Theoretical Probability
Experimental Probability for
10 trials
Difference between
theoretical and experimental
Experimental Probability for
50 trials
Difference between
theoretical and experimental
12. Explain the findings of the table above and how the number of experimental trials is related to
the theoretical probability.
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Part IV: Outcome Grids
13. Define an outcome grid.
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14. Create an outcome grid to determine the theoretical probability for each scenario below.
Color the “successful” outcomes on the grid green and the “unsuccessful” outcomes on the
grid red.
a. Flipping two coins and both are tails.
Outcome Grid
Theoretical Probability:
b. Rolling two dice and having the sum of the rolled numbers be even.
Outcome Grid
Theoretical Probability:
c. Spinning two spinners and one lands on a quadrilateral and one lands on a triangle.
Outcome Grid
Theoretical Probability:
Part V: Class Carnival
You will be working with a partner(s) to create a game for a class carnival. Your game should
demonstrate your knowledge of probability. While you can be creative with your game, remember that
your game must allow you to find theoretical and experimental probabilities, as well as making outcome
grids. When brainstorming carnival games, think about the practicality of calculating probabilities. You
cannot create a game that will not allow you to find probabilities and create outcome grids. Keep in
mind that in order to create an outcome grid, you must have two events in your game, they may be
the same or different.
Use the remainder of the page to brainstorm carnival game ideas. Before beginning to create your
game, you must have it approved by your teacher.
Carnival Booth Record
***Complete this form as you are working your booth.
Contestant Name
# of Wins out of
5 trials
Total number of contestants: _____
Total number of trials (5 per contestant): _____
Total number of wins: _____
Experimental Probability of Winning: _____
Carnival Contestant Record
***Complete this form as you are a contestant playing at other people’s booths.
Booth Name:
Given Theoretical Probability of Winning:
Outcome #1:
Outcome #4:
Outcome #2:
Outcome #5:
Outcome #3:
Total Wins:
Experimental Probability of Winning:
Given Theoretical Probability of Winning:
Booth Name:
Outcome #1:
Outcome #4:
Outcome #2:
Outcome #5:
Outcome #3:
Total Wins:
Given Experimental Probability of Winning:
Booth Name:
Given Theoretical Probability of Winning:
Outcome #1:
Outcome #4:
Outcome #2:
Outcome #5:
Outcome #3:
Total Wins:
Experimental Probability of Winning:
Booth Name:
Given Theoretical Probability of Winning:
Outcome #1:
Outcome #4:
Outcome #2:
Outcome #5:
Outcome #3:
Total Wins:
Experimental Probability of Winning:
How many total outcomes did you have during your Carnival experience? _____
How many total times did you win? _____
What is your experimental probability for your entire Carnival experience? _____
Class Carnival Rubric
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Booth Requirements (Total Points: 20)
o Booth name
 Be creative and appeal to your contestants
o Rules of game and instructions to play
 Be specific, detailed, and clear
o Theoretical probability
 Written as a decimal, percent, and fraction
 Include calculations and explanation
o Outcome Grid
o “Cost” of play and “winning” prize
o Booth Presentation
 Pictures/artwork
 Creative, neat, colorful
____/2
____/3
____/5
____/5
____/2
____/3
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Contestant Record
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Booth Record
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Reflection
____/5
o Answer the following reflection questions in complete sentences. Type or ink.
 What are you concerns or considerations as the game inventor?
 What are you concerns or considerations as the contestant?
 How did your booth’s theoretical probability compare to your experimental
probability as calculated on your “Record” sheet?
 What did you learn from this project? How do you feel about it? Would you
make any changes to the project?
Total Points: ______/45