Part I: Introduction Watch Bill Nye’s Probability Video: https://www.youtube.com/watch?v=Sqq4k50dxbI 1. Define probability ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 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? ____________________________________________________________________________________ What does a probability near 0.5 mean? ____________________________________________________________________________________ What does a probability near 1.0 mean? ____________________________________________________________________________________ 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: ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 5. Define experimental probability ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 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? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 7. Explain the difference between theoretical probability and experiential probability. Use the example of flipping a coin 10 times. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 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. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ Part IV: Outcome Grids 13. Define an outcome grid. ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ 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. Given Theoretical Probability of Winning: Booth Name: 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: Given Theoretical Probability of Winning: Booth Name: 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: 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 - Booth Requirements (Total Points: 20) o Booth name ____/2 . Be creative and appeal to your contestants o Rules of game and instructions to play ____/3 . Be specific, detailed, and clear o Theoretical probability ____/5 . Written as a decimal, percent, and fraction . Include calculations and explanation o Outcome Grid ____/5 o “Cost” of play and “winning” prize ____/2 o Booth Presentation ____/3 . Pictures/artwork . Creative, neat, colorful - Contestant Record ____/10 - Booth Record ____/10 - 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 .