# Order the fractions from least to greatest. Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½

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1 Outcome G

2 Order the fractions from least to greatest Use Benchmark Fractions to help you. First try to decide which is greater than ½ and which is less than ½

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4 Likelihood Certain Most Likely Likely Unlikely Impossible Rate the following: 1. The sun will rise tomorrow 2. Mrs. Ambre will be president in Ms. Vant will teach Science next year. 4. It will rain on April Jenny s average bowling score is 130. She will score 250 on her next game.

5 Likelihood Certain Most Likely Likely Unlikely Impossible Rate the following: 1. The sun will rise tomorrow Certain 2. Mrs. Ambre will be president in 2080 Impossible 3. Ms. Vant will teach Science next year. Most Likely 4. It will rain on April Likely 5. Jenny s average bowling score is 130. She will score 250 on her next game. Unlikely

6 Using a fraction bar, assign percents and fractions to the terms certain, most likely, likely, unlikely and impossible.

7 Using a fraction bar, assign percents and fractions to the terms certain, most likely, likely, unlikely and impossible. Impossible Unlikely As Likely as Not Most Likely Certain 0 4 0% % % % 1 100%

8 Probability of rolling two dice How many total outcomes? What are the chances to roll a 5? Fraction Reduced Fraction Percent What are the chances to roll a 12? Fraction Reduced Fraction Percent Which number has the best chance to be rolled?

9 Probability of rolling two dice How many total outcomes? 36 What are the chances to roll a 5? % Fraction Reduced Fraction Percent What are the chances to roll a 12? % Which number has the best chance to be rolled? 7

10 When we played Face Off, many students put all of their chips on 7. Was this a good idea or a bad idea? Explain your reasoning.

11 Use the Spinner to determine the probability of: P(6) P(not 4 or 5) P(even)

12 3/12 ¼ 25% Use the Spinner to determine the probability of: P(6) 1/8 13% P(not 4 or 5) 6/8 3/4 75% P(even) 4/8 ½ 50%

13 The team members are Daniel, Kayla, Kevin, Matt and Jonathon. Who will be the team captain? P(Daniel) P(girl) P(not Kayla or Matt) P(Cynthia) There are 17 green cubes 3 blue cubes and 5 red cubes P( green) P(blue or red) P(Not purple)

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15 Sample Sets A sample set shows all of the outcomes. You can use an organized chart, a list or a tree diagram

16 An event consists of spinning the spinner shown here and rolling a standard number cube. 1. How many different outcomes are there? 2. What is the probability of the spinner landing on green? 3. What is the probability of rolling an even number on the number cube? 4. What is the probability of the spinner landing on green AND an even number being rolled? 5. What is the probability of the spinner landing on green OR an even number being rolled?

17 An event consists of spinning the spinner shown here and rolling a standard number cube. 1. How many different outcomes are there? What is the probability of the spinner landing on green? 1/3 3. What is the probability of rolling an even number on the number cube? 1/2 4. What is the probability of the spinner landing on green AND an even number being rolled? 1/6 5. Explain how the probability you found in Step 4 is related to the two probabilities you found in Steps 2 and 3?

18 Make a Tree Diagram to show the outcomes

19 What are the outcomes of flipping two coins? Make a list, tree diagram and chart. What if there was a coin and this spinner? What are the outcomes? Make a list, tree diagram and chart.

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24 Fundamental Counting Principle Gina, Maria, Rebecca are looking for a male science partner. They can choose from Henry, Frank, Vince, Sonjay, or Joey. How many different partnerships can be made? Set up your problem like this: x = Number of Females Number of Males Total Partnerships

25 Fundamental Counting Principle Gina, Maria, Rebecca are looking for a male science partner. They can choose from Henry, Frank, Vince, Sonjay, or Joey. How many different partnerships can be made? Set up your problem like this: 3 x 5 = 15 Number of Females Number of Males Total Partnerships

26 Fundamental Counting Principle Three dice will be thrown. How many different outcomes are there? Set up your problem like this: X X = # of sides on a dice # of sides on a dice # of sides on a dice Total Outcomes

27 Fundamental Counting Principle Three dice will be thrown. How many different outcomes are there? Set up your problem like this: X X = Number of sides on a dice Number of sides on a dice Number of sides on a dice Total Outcomes 6

28 Fundamental Counting Principle One coin will be flipped, One 10-sided dice will be thrown and another coin will be flipped. How many different outcomes are there? Set up your problem like this: X X = # of sides on a dice # of sides on a dice # of sides on a dice Total Outcomes

29 Fundamental Counting Principle One coin will be flipped, One 10-sided dice will be thrown and another coin will be flipped. How many different outcomes are there? Set up your problem like this: X X = Number of sides on a coin Number of sides on the dice Number of sides on a coin Total Outcomes

30 Fundamental Counting Principle How many outfits can be made from a brown skirt, red skit, or a plaid skirt, and a white blouse or a grey blouse, and sandals, heels or flats Set up your problem: Lines and words

31 Fundamental Counting Principle How many outfits can be made from a brown skirt, red skit, or a plaid skirt, and a white blouse or a grey blouse, and sandals, heels or flats Set up your problem: X X = Number of Skirts Number of Shirts Number of shoes Total Outfits

32 Calculate the Theoretical Probability (fraction AND percent rounded to the nearest whole percent) 1. If I was going to reach in the box and grab a cupcake, what is the theoretical probability that I would pick Thomas the Tank Engine? 2. What is the theoretical probability that I would pick Hello Kitty? 3. Why do these two answers add up to 100%? 5. What is the theoretical probability that I will choose to wear the floral skirt with the white blouse? 6. What is the theoretical probability that I will not choose the floral skirt, but I will wear the black blouse. Hint! Create a sample set to answer 5 and 6!

33 Create a Sample Set to show the outcomes 1. What is the theoretical probability that I will choose to wear the floral skirt with the white blouse? 2.. What is the theoretical probability that I will not choose the floral skirt, but I will wear the black blouse.

34 Calculate the Theoretical Probability (fraction AND percent rounded to the nearest whole percent) 1. If I was going to reach in the box and grab a cupcake, what is the theoretical probability that I would pick Thomas the Tank Engine? 7/12 58% 2. What is the theoretical probability that I would pick Hello Kitty? 5/12 42% 3. Why do these two answers add up to 100%? Share your answer with your neighbor 5. What is the theoretical probability that I will choose to wear the floral skirt with the white blouse? 1/24 4% 6. What is the theoretical probability that I will not choose the floral skirt, but I will wear the black blouse. 5/24 21%

35 Show the outfit combinations in a list, tree diagram and organized chart for the pants, shirts and jackets.

36 Dependent or Independent? Tell whether each set of events is independent or dependent. Explain your answer. A dime lands heads up and a nickel lands heads up. You choose a colored game piece in a board game, and then your sister picks another color. Rolling two odd numbers on two dice. Choosing a vegetable topping and a meat topping on your pizza. Choosing a student from a group of 10 kids, then choosing another student. Taking a \$1 bill out of your wallet with 5 singles, 5 fives and 3 tens. Then choosing another one dollar bill. A number cube lands showing an odd number. It is rolled a second time and lands showing 6. Flipping two different coins and each coin landing showing tails. Flipping the same coin twice and each coin landing on tails.

37 Tell whether each set of events is independent or dependent. Explain your answer. 1. A dime lands heads up and a nickel lands heads up. Independent 2. You choose a colored game piece in a board game, and then your sister picks another color. Dependent 3. Rolling two odd numbers on two dice. Independent 4. Choosing a vegetable topping and a meat topping on your pizza. Independent (can you make an argument for dependent?) 5. Choosing a student from a group of 10 kids, then choosing another student. Dependent 6. Taking a \$1 bill out of your wallet with 5 singles, 5 fives and 3 tens. Then choosing another one dollar bill. Dependent 7. A number cube lands showing an odd number. It is rolled a second time and lands showing 6. Independent 8. Flipping two different coins and each coin landing showing tails. Independent 9. Flipping the same coin twice and each coin landing on tails. Independent

38 1. Use the Fundamental Counting Principle to find the number of outcomes for picking one ticket from each pile. 2. Make a tree diagram to show the outcomes of picking a ticket from each pile. Use the labels ~ Start, ticket #1, ticket #2, ticket #3. 3. Make an organized chart to show the outcomes of picking a ticket from each pile.

39 1. Use the Fundamental Counting Principle to find the number of outcomes for picking one ticket from each pile. 2. Make a tree diagram to show the outcomes of picking a ticket from each pile. Use the labels ~ Start, ticket #1, ticket #2, ticket #3. 3. Make an organized chart to show the outcomes of picking a ticket from each pile.

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41 What is the probability of each of the following events when two fair number cubes are rolled? 1. p(7 or 10) 2. P(not a 6) 3. P(odd number) 4. P(even number) 5. P(higher than 10) (should you include 10?) 6. If three number cubes are rolled, what is the chance of rolling triple 3 s?

42 What is the probability of each of the following events when two fair number cubes are rolled? 1. p(7 or 10) 1/4 2. P(not a 6) 31/36 3. P(odd number) 1/2 4. P(even number) 1/2 5. P(higher than 10) 1/12 (should you include 10?) 6. If three number cubes are rolled, what is the chance of rolling triple 3 s? 1/216

43 The theoretical probability of spinning a red is 1/6 or I should spin a red 17% of the time. When I ran the experiment, my experimental probability was 5/18 or 28%. 1. How many times did I run the experiment? 2. How many times did I get the desired results (red)? 3. Why are the TP and the EP different percentages? 4. How many times should I expect to spin a red, based on the EP, if I ran the experiment 40 times? 5. What is the difference between TP and EP?

44 The theoretical probability of spinning a red is 1/6 or I should spin a red 17% of the time. When I ran the experiment, my experimental probability was 5/18 or 28%. 1. How many times did I run the experiment? How many times did I get the desired results? 5 1. Why are the TP and the EP different percentages? 2. What is EP of spinning a red if I ran the experiment 40 times? 11 or 11.1? 5. What is the difference between TP and EP?

45 Experiment: I have a cup with 5 marbles ~ 2 blue, 2 red and one yellow. I also have a dice with six sides ~ +3, +5, -1, +4, -2, +3. What is the Theoretical Probability that I will pull a red marble and roll a positive number? P(red, positive) If I do this experiment 25 times, how many times to you think I will get the desired results? Why do you think that? Lets do it. Make a chart to keep track to the outcomes on your paper. Based on the Experimental probability, how many times to you predict that you will get the desired results after 110 tries?

46 Experimental Probability (EP) Experiments What do you THINK will happen if you run this experiment 25 times? Use the theoretical probability (TP) to make a good estimate. Make a tally chart to keep track as you run the experiment. Compare your EP to your estimate from your TP

47 Experimental Probability When the students came in my room, 18 were wearing blue jeans and 6 were wearing shorts. What is the chance that the next person that comes in will be wearing blue jeans? Gwen eats Cheerios for breakfast 4 out of every 5 days. How many days do you think Gwen ate Cheerios in April? Marcus made his free throws 20 out of 25 times. What is the chance he will make the next free throw?

48 Experimental Probability When the students came in my room, 18 were wearing blue jeans and 6 were wearing shorts. What is the chance that the next person that comes in will be wearing blue jeans? 18/24 or 3/4 Gwen eats Cheerios for breakfast 4 out of every 5 days. How many days do you think Gwen ate Cheerios in April? 24 days Marcus made his free throws 20 out of 25 times. What is the chance he will make the next free throw? 80%

49 Find the Theoretical Probability Answer as a fraction 1. p(green) 2. P(blue) 3. P(not green) 4. P(not blue or green) Answer as a percent 5. P(white) 6. P(not white) 7. P(solid) 8. P(zebra or solid) 9. P(polka dot)

50 1. p(green) 5/12 2. P(blue) 1/3 3. P(not green) 7/12 4. P(not blue or green) 1/4 5. P(white) 40% 6. P(not white) 60% 7. P(solid) 60% 8. P(zebra or solid) 100% 9. P(polka dot) 0%

51 Based on my results, if I rolled the dice 300 times, how many times would I expect to roll a 3? What about 5 or 6? Experimental Probability I rolled the dice 50 times, here are my results. Number Times Rolled Based on my results, if I rolled the dice 84 times, how many times would I expect to roll a 1? What about 5?

52 Experimental Probability I rolled the dice 50 times, here are my results. Number Times Rolled Based on my results, if I rolled the dice 84 times, how many times would I expect to roll a 1? 20 times What about 5? 8 times Based on my results, if I rolled the dice 300 times, how many times would I expect to roll a 3? 48 times What about 5 or 6? 84 times

53 Students at Drauden Point 6 th Grade 274 Students 7 th Grade 280 Students 8 th Grade 266 student Boys 380 Girls 440 How many students are at Drauden Point? If Mr. Flynn was going to pick a student at random, find the probability that it will be: 1. a 7 th grader. 2. Not an 8 th Grader 3. A girl 4. A 7 th grade boy 5. An 8 th grade girl

54 Students at Drauden Point 6 th Grade 274 Students 7 th Grade 280 Students 8 th Grade 266 student Boys 380 Girls 440 How many students are at Drauden Point? 820 If Mr. Flynn was going to pick a student at random, find the probability that it will be: 1. a 7 th grader. 14/41 2. Not an 8 th Grader 277/410 68% 3. A girl 22/41 54% 4. A 7 th grade boy 266/ % 5. An 8 th grade girl 17% 1463/8405

55 Based on my results, if I rolled the dice 90 times, how many times would I expect to roll a 3? What about 5 or 6? Experimental Probability I rolled the dice 50 times, here are my results. Number Times Rolled Based on my results, if I rolled the dice 150 times, how many times would I expect to roll a 1? What about 4?

56 Based on my results, if I rolled the dice 90 times, how many times would I expect to roll a 3? 18 times What about 5 or 6? 27 times Experimental Probability I rolled the dice 50 times, here are my results. Number Times Rolled Based on my results, if I rolled the dice 150 times, how many times would I expect to roll a 1? 30 times What about 4? 24 times

57 Dependent Events 1) The digits 0-9 are each written on a slip of paper and placed in a hat. Two slips of paper are randomly selected without replacing the first. What is the probability that the number 0 is drawn first and then a 7 is drawn 2) Francesca randomly selects two pieces of fruit from a basket containing 8 oranges and 4 apples without replacing the first fruit. Find the probability that she selects two oranges. 3) A jar has 15 marbles: 3 red, 5 blue, and 7 green. A marble is selected and not returned before another marble is selected. What is the probability of selecting a red and then green marble?

58 1. P(blue) 2. P(green) 3. P(blue or orange) 4. P (blue then green) with replacement 5. P (blue then orange) with replacement Write your answers first as fractions. Once you finish them all then convert to percents 6. P (orange, green) with replacement 7. P (blue, blue) with replacement 8. P (blue then green) without replacement 9. P (blue then orange) without replacement 10. P (orange, green) without replacement 11. P (blue, blue) without replacement 12. Which of the above are dependent and independent events?

59 1. P(blue) 1/3 2. P(green) 5/12 3. P(blue or orange) 7/12 4. P (blue then green) with replacement 5/36 5. P (blue then orange) with replacement 1/12 6. P (orange then green) with replacement 5/48 7. P (blue then blue) with replacement 1/9 8. P (blue then green) without replacement 5/33 9. P (blue then orange) without replacement 1/ P (orange then green) without replacement 5/ P (blue then blue) without replacement 1/ Which of the above are dependent and independent events?

60 1. On which spinner (one or two) are the chances equally likely? What is the chance (written as a fraction and percent) 2. Describe the chances (fraction) of spinning each section on spinner two ~ your denominator will NOT always be four. What will it be? Gold: Orange: Blue: Grey: 3. How many outcomes of spinning spinner one then two are there? Are the outcomes equally likely? Why/why not? 4. What is the chance of spinning each of the following: p (blue and gold) p (orange and grey) p (grey and blue) p (not blue and gold) p (not grey and not blue) 4. Are these two spinners independent or dependent events.

61 1. 1. On which spinner (one or two) are the chances equally likely? What is the chance (written as a fraction and percent) 1 ¼ and 25% 2. Describe the chances (fraction) of spinning each section on spinner two ~ your denominator will NOT always be four. What will it be? Gold: ¼ 25% Orange: ¼ 25% Blue: 1/8 12.5% Grey: 3/8 37.5% How many outcomes of spinning spinner one then two are there? Are the outcomes equally likely? Why/why not? 8. Not equally likely bc there is a greater chance of spinning grey on the second spinner. 4. What is the chance of spinning each of the following: p (blue and gold) 1/16 p (orange and grey) 1/16 p (grey and blue) 3/32 p (not blue and gold) 3/16 p (not grey and not blue) 21/32 4. Are these two spinners independent or dependent events. Independent

62 Can you determine different meal choices there are? A three course dinner can be made from the following items: Appetizer: soup or salad Entrée: Steak, chicken, or fish Dessert: Carrot cake or cheese cake Make a sample space (list, tree or chart) to show all of the possible menu combinations

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