1. Probability

2. Probability The ratio of favorable outcomes to possible outcomes, or in other words the likelihood (or chance) that something will happen The ratio of favorable outcomes to possible outcomes, or in other words the likelihood (or chance) that something will happen Can be represented as a fraction (ratio), percent, or decimal Can be represented as a fraction (ratio), percent, or decimal 2 Types: 2 Types: –Theoretical –Experimental

3. Probability Theoretical Experimental

4. Theoretical Probability Determined through mathematical means Determined through mathematical means Example: What is the probability of obtaining tails when flipping a coin? Example: What is the probability of obtaining tails when flipping a coin?

5. Citation (MLA) Discovering Math: Probability (Grades 6-8). Discovery Channel School. 2006. unitedstreaming. 3 June 2008 Visit http://www.unitedstreaming.com and view a video segment from the video Discovering Math: Probability (Grades 6-8) called Example 2: Multiple Events--Number Cubes Visit http://www.unitedstreaming.com and view a video segment from the video Discovering Math: Probability (Grades 6-8) called Example 2: Multiple Events--Number Cubeshttp://www.unitedstreaming.comDiscovering Math: Probability (Grades 6-8) http://www.unitedstreaming.comDiscovering Math: Probability (Grades 6-8)

6. Experimental Probability Obtained through experiments, simulations, or data Obtained through experiments, simulations, or data Example: Flip a coin 50 times, record the number of times tails is obtained, and determine the probability of obtaining tails based on the experiment. Example: Flip a coin 50 times, record the number of times tails is obtained, and determine the probability of obtaining tails based on the experiment.

7. Citation (MLA) Discovering Math: Probability (Grades 6-8). Discovery Channel School. 2006. unitedstreaming. 3 June 2008 Visit http://www.unitedstreaming.com and view a video segment from the video Discovering Math: Probability (Grades 6-8) called Example 1: Historical Probability—Basketball Free Throws Visit http://www.unitedstreaming.com and view a video segment from the video Discovering Math: Probability (Grades 6-8) called Example 1: Historical Probability—Basketball Free Throwshttp://www.unitedstreaming.comDiscovering Math: Probability (Grades 6-8) http://www.unitedstreaming.comDiscovering Math: Probability (Grades 6-8)

8. Differences What would make theoretical probabilities and experimental probabilities differ? What would make theoretical probabilities and experimental probabilities differ? What needs to be done to bring an experimental probability closer to a theoretical probability? What needs to be done to bring an experimental probability closer to a theoretical probability?

9. Experimental Probability Examples Susie kicked corner kicks at soccer practice. Out of her 100 attempts, her experimental probability of getting a goal was 55%. How many goals did she make? Susie kicked corner kicks at soccer practice. Out of her 100 attempts, her experimental probability of getting a goal was 55%. How many goals did she make? Answer 1

10. Based on the data below, what is the experimental probability that a student from this school received an overall score of a C for the first 9 weeks? Based on the data below, what is the experimental probability that a student from this school received an overall score of a C for the first 9 weeks? Student’s Overall Scores for the first 9 Weeks of the School Year Class Red Class Blue Class Orange Class Green A14% 20% 18% 10% B 22% 24% 20% 18% C36% 41% 32% 44% D 18% 10% 22% 16% F 10% 5% 8% 12% Answer 2

11. The results of rolling a six-sided die 140 times are given below. The results of rolling a six-sided die 140 times are given below. Results from Rolling a Die 140 Times Number on die123456 No. of Occurrences202124212628 a.) Find the theoretical probability of rolling a 4 on a six-sided die. b.) Find the experimental probability based on the given data of rolling a 4 on a six-sided die. Answer 3

12. Let’s conduct our own simulations and find the respective probabilities. Let’s conduct our own simulations and find the respective probabilities. Simulation Time!

13. The End

14. Answer 1 55 55 Next Example

15. Answer 2 153/400 or about 38% 153/400 or about 38% Next Example

16. Answer 3 a.) 1/6 a.) 1/6 b.) 21/140 = 3/20 or 15% b.) 21/140 = 3/20 or 15% Simulation Slide