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Probability (Unit 5) Is the likelihood or chance of an even occurring. Favourable Outcomes Total Possible Outcomes What is the probability of rolling the number 2 on a dice? How many favourable outcomes? How many possible outcomes? Place these numbers into the fraction above…

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How to express probability Probability can be written in 3 ways... As a fraction = 1/6 As a decimal = 0.16 As a percent 0.16 x 100% = 16% How often will the number 2 show up when rolled?

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Determine the probability First you must find the possible outcomes (total) and then the favourable outcomes (what you’re looking for). Then place them into the probability equation. 1.Rolling an even number on a dice? 2.Pulling a red card out from a deck of cards? 3.Using a four colored spinner to find green? 4.Selecting a girl from your class? Favourable Outcomes Total Possible Outcomes

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Determine the probability A cookie jar contains 3 chocolate chip, 5 raisin, 11 Oreos, and 6 almond cookies. Find the probability if you were to reach inside the cookie jar for each of the cookies above. Type of Cookie Chocolate Chip RaisinOreoAlmond Fraction Decimal Percent Ratio

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Determine the probability Page 163: # 3ab, 5, 7 Page 164: # 9

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Organized Outcomes Independent Events: The outcome of one event has not effect on the outcome of another event Example: ROCK PAPER SCISSOR Tails Head

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Organized Outcomes Sample Space: All possible outcomes of an experiment What is the probability of Paper/Head? What is the probability of tails showing up? Sample Space HeadTail Rock Paper Scissor

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“Tree Diagram” “Tree Diagram” to represent Outcomes HTHT R P S Coin Flip Rock, Paper, Scissor H, RockT, Rock H, PaperT, Paper H, ScissorT, Scissor Outcome

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“Spider Diagram” “Spider Diagram” to represent Outcomes Rock Paper Scissor

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Organized Outcomes You can find the sample space of two independent events in many ways. 1.Chart 2.Tree Diagram 3.Spider Diagram Your choice, but showing one of the above illustrates that you can find the favourable and possible outcomes for probability.

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Organized Outcomes Page 169: # 5, 8 Page 170: # 9, 10

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Probabilities of Simple Independent Events Random: an event in which every outcome has an equal chance of occurring. A school gym has three doors on the stage and two back doors. During a school play, each character enters through one of the five doors. The next character to enter can be either a boy or a girl. Use a “Tree Diagram” to determine to show the sample space. Then answer the questions on the next slide!

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Probabilities of Simple Independent Events Random: an event in which every outcome has an equal chance of occurring. See Page 172 for your “Tree Diagram” of the school gym doors!

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Using a Table to DETERMINE Probabilities How to determine probabilities: Use “p” (or any other letter as the variable to represent what you’re looking for) and divide it by “t” the total outcomes. Then multiply your answer by 100%. Equation stays the same: p/t x 100% Use your results from the “tree diagram” of the gym doors and place them into a table. Then determine the probabilities for the scenarios on the next slide!

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Using a Table to DETERMINE Probabilities How to determine probabilities: p/t x 100% Back Left (BL) Back Right (BR) Left Stage (LS) Centre Stage (CS) Right Stage (RS) BoyBBLBBRBLSBCSBRS GirlGBLGBRGLSGCSGRS Determine the probability for the scenarios below... 1. Of a boy using any right door? 2. Of anyone (boy or girl) using a stage door? 3. Of a girls using any of the doors?

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Determine Probabilities Page 175: # 6, 8 Page 176: # 13

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Applications Applications of Independent Events Use Tree Diagrams, Charts or other graphic organizers to solve probability problems. How can you win at the game of “ Sit & Save ?” RULES: 1.Stand up at the beginning of the round. 2.Two dice are rolled each round. You may collect the sum of your dice as long as a “6” does NOT appear. A “6” means all numbers before are cancelled and you get zero for that round. 3.After each roll you have two choices Continue standing and roll again…hoping for no “6” Sit and collect your total points!

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Applications Applications of Independent Events How can you win at the game of “ Sit & Save ?” 1.Who had the highest score? 2.What is the possibility of a 6 appearing with 2 dice? (sample data) 3.Use the numbers above for each player to find who had the best probability (percent) of not rolling a 6. Student Names Round 1Round 2Round 3Round 4TOTAL

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Interpret Interpret Outcomes Use Tree Diagrams, Charts or other graphic organizers to solve probability problems. 1.What are the 2 independent events? 2.What is the probability of the sum of these 2 events ending up to total “4”… 3.What is the probability of outcome having one 3 appear?

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Interpret Interpret Outcomes 1.What is the probability of red appearing? 2.What is the possibility of a black and green appearing? 3.What is the possibility of both events being two syllable words appearing?

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Interpret Interpret Independent Outcomes Page 181: # 6, 7 Page 182: # 9

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Theoretical vs. Practical Theoretical vs. Practical Probabilities What are the chances of a boy and girl picking the same number from 1-5. Try this 10 times and tally your results (Practical). Then compare to your “theoretical answer.” Boy Girl Boy Girl Boy Girl Boy Girl Boy Girl 12345 BoyB1B2B3B4B5 GirlG1G2G3G4G5 Practical Theoretical

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Theoretical vs. Practical Theoretical vs. Practical Probabilities What are the chances of a boy and girl picking the same number from 1-5. Try this 10 times and tally your results (practical). Then compare to your “theoretical” answer. Boy Girl Boy Girl Boy Girl Boy Girl Boy Girl 12345 BoyB1B2B3B4B5 GirlG1G2G3G4G5 Practical Theoretical The probability of an event occurring based on experimental results. The expected probability of an event occurring.

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TESTED Are your ready to be TESTED on “Probability?” We have covered a lot of material in this unit. Do you have any concerns or questions about any of the topics below? 1.Representing probability in different ways… (Pg. 158) 2.Types of sample spaces to find the probability (Pg. 166-167) 3.Explain how to identify an independent event. 4.Determine the outcomes of two independent events. (Pg. 172) 5.Find the sum of different events…which sample space would be best to use? 6.Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6) 7.Use diagrams to interpret data and probabilities. (Pg. 178-179) 8.Compare experimental to theoretical probabilities. (Pg. 184) If so, then you are ready for the test. For more practice and review of the test please complete questions on page 190-191 (5, 8, 9, 12, and 13). Make sure to check your answers to the back of the book so you are prepared for the exam. As well, if you have any questions please see me in the morning or at lunch before the exam! For extra practice complete the “Practice Test” on pages 192-193. Best of luck!

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