Probability and Statistics Is it Fair or Unfair Teacher Quality Grant

What does it mean to be fair?

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

1.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 2.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? 3.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 1.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). 2.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 4.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 5.For each of the three colors, find the probability that you will draw that color. 11/16 ; 1/16 7.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 11.Fair 12. Unfair 13. Fair

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