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## Probability and Statistics Is it Fair or Unfair

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**Probability and StatisticsIs it Fair or Unfair**Teacher Quality Grant**Activity 1: Fair and Unfair Games**• Have you ever felt that a game you were playing wasn't fair but you weren't sure why? • You can use probability to decide whether a game is fair or unfair.**Activity 1: Fair and Unfair Games**• A spinner has 8 equal sections. Four sections are gray, three are white, and one is blue. Keri and Josh use the spinner to play a game. The rules are: • Players alternate turns. • Keri gets a point if she lands on gray or blue. • Josh gets a point if he lands on white or blue. • First player to earn 10 points wins.**Activity 1: Fair and Unfair Games**• Josh lost the first game and said the game wasn't fair. Keri said the 8 sections were equal, so the game was fair. What do you think of her argument? Does it prove that the game is fair? • If you were playing this game, would you take the gray and blue sections or the white and blue sections? Why?**Activity 1: Fair and Unfair Games**Try this: 1. Shane and Amanda play a number cube game. Shane gets a point if he rolls a number evenly divisible by 2. Amanda gets a point if she rolls a number evenly divisible by 3. Is the game fair? Explain.**Activity 1: Fair and Unfair Games**Draw Conclusions: 1. Change one rule in Keri and Josh’s game to make the game fair.**Activity 2: Fair and Unfair Games**Activity 2: • This activity is also included on the PDF with Activity 1 complete the activity in groups of 3. • Your group is taking on the rolls of Kara, Derik, and Heather in the activity.**Activity 3: Fair and Unfair Games**Activity 3: • Materials: Cubes • Get into groups of 3 and complete the activity 3**Activity 3: Fair and Unfair Games**• Suppose you tossed a number cube. Which outcome would be more likely, a 5 or an even number? Explain your reasoning. • an even number; there are three even numbers you could toss (2, 4, 6) but only one 5 (5). • Toss a number cube 20 times. Record the number of times you roll a 5 and the number of times you roll an even number. • Because there are three even numbers but only one 5, students will probably roll an even number more often than they roll a 5.**Activity 3: Fair and Unfair Games**3. Do the results of your experiment in Step 2 confirm your reasoning in Step 1? Explain • Blue is most likely because there are more blue marles than any other color. Green is the last likely because there are fewer green marbles than any other color**Activity 3: Fair and Unfair Games**• If you withdraw one marble from the bag at random, which is the most likely color that you will draw? Which is the least likely? Explain. • blue: 11/16 ; red: 4/16 ; green: 1/16 • For each of the three colors, find the probability that you will draw that color. • 11/16 ; 1/16 • Of the three probabilities, which is greatest? Which is least? • Event B**Activity 3: Fair and Unfair Games**9. no; Sector 3 is bigger than the other two sections, so it is more likely that you will spin 3 than either of the other two numbers. Sector 2 is smaller than the other two sections, so it is less likely that you will spin 2 than either of the other two numbers. 10. agree; because Sector 3 is bigger than the other sectors, Joey has a better chance of winning than either Mark or Kenny has.**Activity 3: Fair and Unfair Games**13. Fair 12. Unfair • Fair**More Activities**• Lesson Plan • http://www.learnnc.org/lp/pages/3786 • Racing Game • Racing Game Field • Pig Games • Greedy Pig Dice Game • Pig Dice Game