Presentation on theme: "Probability (Unit 5) Is the likelihood or chance of an even occurring."— Presentation transcript:
1 Probability (Unit 5) Is the likelihood or chance of an even occurring. Favourable OutcomesTotal Possible OutcomesWhat is the probability of rolling the number 2 on a dice?How many favourable outcomes?How many possible outcomes?Place these numbers into the fractionabove…
2 How to express probability Probability can be written in 3 ways...As a fraction = 1/6As a decimal = 0.16As a percent0.16 x 100% = 16%How often will thenumber 2 show upwhen rolled?
3 Determine the probability First you must find the possible outcomes (total) and thenthe favourable outcomes (what you’re looking for). Thenplace them into the probability equation.Rolling an even number on a dice?Pulling a red card out from a deck of cards?Using a four colored spinner to find green?Selecting a girl from your class?Favourable OutcomesTotal Possible Outcomes
4 Determine the probability A cookie jar contains 3 chocolate chip, 5 raisin, 11 Oreos,and 6 almond cookies. Find the probability if you were toreach inside the cookie jar for each of the cookies above.Type of CookieChocolate ChipRaisinOreoAlmondFractionDecimalPercentRatio
5 Determine the probability Page 163: # 3ab, 5, 7Page 164: # 9
6 Organized Outcomes Independent Events: The outcome of one event has not effect on the outcome of another eventExample:ROCKPAPERSCISSORTails Head
7 Organized Outcomes Sample Space: All possible outcomes of an experimentWhat is the probability of Paper/Head?What is the probability of tails showing up?Sample SpaceHeadTailRockPaperScissor
8 “Tree Diagram” to represent Outcomes H TCoin FlipR P S R P SRock, Paper, ScissorH, Rock T, RockH, Paper T, PaperH, Scissor T, ScissorOutcome
9 “Spider Diagram” to represent Outcomes RockRockPaperPaperScissorScissor
10 Organized Outcomes You can find the sample space of two independent events in many ways.ChartTree DiagramSpider DiagramYour choice, but showing one of the aboveillustrates that you can find the favourable andpossible outcomes for probability.
12 Probabilities of Simple Independent Events Random:an event in which every outcome has an equal chance ofoccurring.A school gym has three doors on the stage and two backdoors. During a school play, each character enters throughone of the five doors. The next character to enter can beeither a boy or a girl. Use a “Tree Diagram” to determineto show the sample space. Then answer the questions onthe next slide!
13 Probabilities of Simple Independent Events Random:an event in which every outcome has an equal chance ofoccurring.See Page 172 for your “Tree Diagram” of the school gymdoors!
14 Using a Table to DETERMINE Probabilities How to determine probabilities:Use “p” (or any other letter as the variable to representwhat you’re looking for) and divide it by “t” the totaloutcomes. Then multiply your answer by 100%.Equation stays the same: p/t x 100%Use your results from the “tree diagram” of the gym doorsand place them into a table. Then determine theprobabilities for the scenarios on the next slide!
15 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)BoyBBLBBRBLSBCSBRSGirlGBLGBRGLSGCSGRSDetermine 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?
17 Applications of Independent Events Use Tree Diagrams, Charts or other graphic organizers tosolve probability problems.How can you win at the game of “Sit & Save?”RULES:Stand up at the beginning of the round.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.After each roll you have two choicesContinue standing and roll again…hoping for no “6”Sit and collect your total points!
18 Applications of Independent Events How can you win at the game of “Sit & Save?”Who had the highest score?What is the possibility of a 6 appearing with 2 dice? (sample data)Use the numbers above for each player to find who had the best probability (percent) of not rolling a 6.Student NamesRound 1Round 2Round 3Round 4TOTAL
19 Interpret OutcomesUse Tree Diagrams, Charts or other graphic organizers to solveprobability problems.What are the 2 independent events?What is the probability of the sum of these 2 events ending up to total “4”…What is the probability of outcome having one 3 appear?
20 Interpret Outcomes What is the probability of red appearing? What is the possibility of a black and green appearing?What is the possibility of both events being two syllable words appearing?
22 Theoretical vs. Practical Probabilities What are the chances of a boy and girl picking the same numberfrom Try this 10 times and tally your results (Practical) . Thencompare to your “theoretical answer.”PracticalBoyGirlTheoretical12345BoyB1B2B3B4B5GirlG1G2G3G4G5
23 The expected probability of an event occurring. Theoretical vs. Practical ProbabilitiesWhat are the chances of a boy and girl picking the same numberfrom Try this 10 times and tally your results (practical) . Thencompare to your “theoretical” answer.PracticalThe probability of an event occurring based on experimental results.BoyGirlThe expected probability of an event occurring.Theoretical12345BoyB1B2B3B4B5GirlG1G2G3G4G5
24 Are your ready to be TESTED on “Probability?” We have covered a lot of material in this unit. Do you have anyconcerns or questions about any of the topics below?Representing probability in different ways… (Pg. 158)Types of sample spaces to find the probability (Pg )Explain how to identify an independent event.Determine the outcomes of two independent events. (Pg. 172)Find the sum of different events…which sample space would be best to use?Solve multiple probabilities… P(1,B) or P(Girls, Boys, 6)Use diagrams to interpret data and probabilities. (Pg )Compare experimental to theoretical probabilities. (Pg. 184)If so, then you are ready for the test. For more practice and review of the test pleasecomplete questions on page (5, 8, 9, 12, and 13). Make sure to check youranswers to the back of the book so you are prepared for the exam. As well, if you haveany questions please see me in the morning or at lunch before the exam! For extrapractice complete the “Practice Test” on pages Best of luck!