Probability What is the probability of rolling the number 2 on a dice? Student Outcome: I will be able to write probabilities as ratios, fractions and percents. Probability: is the likelihood or chance of an event occurring. Outcome: any possible result of a probability event. Favourable Outcome: a successful result in a probability event. (ex: rolling the #1 on a die) Possible Outcome: all the results that could occur during a probability event (ex: rolling a die - - #1, #2, #3, #4, #5, #6) P = Favourable Outcomes Possible Outcomes What is the probability of rolling the number 2 on a dice? What is the favourable outcome? How many possible outcomes?

How to express probability Student Outcome: I will be able to write probabilities as ratios, fractions and percents. 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?

Determine the probability Student Outcome: I will be able to write probabilities as ratios, fractions and percents. First you must find the possible outcomes (all possibilities) and then the favourable outcomes (what you’re looking for). Then place them into the probability equation. Rolling an even number on a die? Pulling a red card out from a deck of cards? Using a four colored spinner to find green? Selecting a girl from your class? P = Favourable Outcomes Possible Outcomes

Determine the probability Student Outcome: I will be able to write probabilities as ratios, fractions and percents. 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 Raisin Oreo Almond Fraction Decimal Percent Ratio

Determine the probability Student Outcome: I will be able to write probabilities as ratios, fractions and percents. 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 Raisin Oreo Almond Fraction 3/25 5/25 11/25 6/25 Decimal 0.12 0.25 0.44 0.24 Percent 12% 25% 44% 24% Ratio 3:25 5:25 11:25 6:25

Determine the probability Page 163-164 # 3, 5, 7, 10 Extend: Page 163 #11, 12

Letter tiles for the word CINCINNATI are placed in a bag. Practical Quiz #1 Letter tiles for the word CINCINNATI are placed in a bag. What is the probability of drawing the letter C? What is the probability of drawing the letter N? What is the probability of drawing the letter O?

Organized Outcomes Independent Events: Student Outcome: I will be able to create a sample space involving 2 independent events. Independent Events: The outcome of one event has no effect on the outcome of another event Example: ROCK PAPER SCISSOR Tails Head

Chart Sample Space: All possible outcomes of an event/experiment Student Outcome: I will be able to create a sample space involving 2 independent events. Sample Space: All possible outcomes of an event/experiment (all the combinations) coin hand What is the probability of Paper/Head? What is the probability of tails showing up? Sample Space Head Tail Rock Paper Scissor

“Tree Diagram” to represent Outcomes Student Outcome: I will be able to create a sample space involving 2 independent events. H T Coin Flip R P S R P S Rock, Paper, Scissor H, Rock T, Rock H, Paper T, Paper H, Scissor T, Scissor Outcomes

“Spider Diagram” to represent Outcomes Student Outcome: I will be able to create a sample space involving 2 independent events. Rock Rock Paper Paper Scissor Scissor

Organized Outcomes You can find the sample space of two independent Student Outcome: I will be able to create a sample space involving 2 independent events. You can find the sample space of two independent events in many ways. Chart Tree Diagram Spider Diagram Your choice, but showing one of the above illustrates that you can find the favourable and possible outcomes for probability.

Organized Outcomes Page 169-170 #5, 8, 9, 10 Extend: Page 170 #13, 14

Probabilities of Simple Independent Events Student Outcome: I will learn about theoretical probability. Random: an event in which every outcome has an equal chance of occurring. Problem: 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!

Probabilities of Simple Independent Events Student Outcome: I will learn about theoretical probability. 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!

Using a Table to DETERMINE Probabilities Student Outcome: I will learn about theoretical probability. How to determine probabilities: Probability (P) = favourable outcomes possible outcomes = decimal x 100% Use your results from the “tree diagram” of the gym doors and place them into a chart. Then determine the probabilities for the chart.

Using a Table to DETERMINE Probabilities Student Outcome: I will learn about theoretical probability. Back Left (BL) Back Right (BR) Left Stage (LS) Centre Stage (CS) Right Stage (RS) Boy B-BL B-BR B-LS B-CS B-RS Girl G-BL G-BR G-LS G-CS G-RS 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?

Determine Probabilities Page 175-176 #6, 9, 12, 13 Extend: Page 176 #14

Rolling a 4 sided die and flipping a quarter. Practical Quiz #2 On the front of the paper: Draw a sample space using a chart for the following events. On the back of the paper: Draw a sample space using a tree diagram for the following events. Rolling a 4 sided die and flipping a quarter.

Applications of Independent Events Student Outcome: I will learn about theoretical probability. Let’s play “Sit & Save?” (page 177) 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 choices Continue standing and roll again…hoping for no “6” OR Sit and collect your total points!

Applications of Independent Events Student Outcome: I will learn about theoretical probability. 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. Round 1 Round 2 Round 3 Round 4 Round 5 Total

Round 1 Round 2 Round 3 Round 4 Round 5 Total Round 1 Round 2 Round 3 Round 4 Round 5 Total

Student Outcome: I will learn about theoretical probability. Interpret Outcomes Student Outcome: I will learn about theoretical probability. Use Tree Diagrams, Charts or other graphic organizers to solve probability problems. What are the 2 independent events? What is the probability of the sum of these 2 events adding up to total “4”… What is the probability of outcome having one 3 appear?

Student Outcome: I will learn about theoretical probability. Interpret Outcomes Student Outcome: I will learn about theoretical probability. What is the probability of red appearing? What is the possibility of a black and green appearing? 3. What is the possibility of brown mirror appearing?

Interpret Independent Outcomes Page 181-182 #4, 6, 8, 9 Extend: Page 182 #11

The expected probability of an event occurring. Theoretical vs. Experimental Probabilities Student Outcome: I will be able to compare experimental and theoretical probability. What are the chances of a boy and girl picking the same number from 1-5. Try this 10 times and tally your results (experimental). Then compare to your “theoretical” answer. experimental The probability of an event occurring based on experimental results. A tally chart will be required. Boy Girl The expected probability of an event occurring. Theoretical 1 2 3 4 5 Boy B1 B2 B3 B4 B5 Girl G1 G2 G3 G4 G5

Theoretical vs. Experimental Probabilities Student Outcome: I will be able to compare experimental and theoretical probability. You must complete 2 of the 3 activities listed. For each activity you must compare the theoretical and experimental probabilities. Each experimental probability must be done 50 times. Then compare to your “theoretical” answer. Activities Flipping a coin and using a spinner. Rolling one 6-sided die and dropping a cup. Rolling two 6-sided dice.

Theoretical vs. Experimental Probabilities Page 187-189 # 4, 6, 7, 9, 11

Practical Quiz #3 When these two independent event are done at the same time, What is the probability of getting: a)anything with red? b) orange-tails?

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? Representing probability in different ways… (Pg. 158) Types of sample spaces to find the probability (Pg. 166-167) 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. 178-179) Compare experimental to theoretical probabilities. (Pg. 184) Outcome – any possible result of a probability experiment. Favourable Outcome – a successful result in a probability experiment. Probability – the likelihood of an event happening. Random – when every result has an equal chance of occurring. Sample Space – all possible outcomes of a probability experiment. Tally Chart – an area to record information during experimental probability.

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? Representing probability in different ways… (Pg. 158) Types of sample spaces to find the probability (Pg. 166-167) 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. 178-179) Compare experimental to theoretical probabilities. (Pg. 184)

Chapter Review Page 190 – 191 #1-14

Handout playing field to students and dice. Game – Baseball Dice Handout playing field to students and dice.