3-52.  Janine’s teacher has presented her with an opportunity to raise her grade: She can roll a special dice and possibly gain points.  If Janine rolls a positive number, she will gain the number of points indicated on the dice.  However, if she rolls a negative number, then she will lose that many points. Janine does not know what to do!  The dice, formed when the net at right is folded, offers four sides that will increase her number of points and only two sides that will decrease her grade.  She needs your help to determine if this dice is fair. What are the qualities of a fair game?  How can you tell if a game is fair?  Discuss this with your team and be ready to share your ideas with the class. The expected value is zero for a fair game. What is the expected value of one roll of this dice?  Show how you got your answer.  Is this dice fair? 3 6 2 + 2 6 −4 + 1 6 1 =− 1 6 ; No, it is not fair. Change only one side of the dice in order to make the expected value 0. Ex: Change the 1 to a 2. What does it mean if a dice or spinner has an expected value of 0? If the expected value is 0, then it is equally likely to win or lose because after that many rolls there would be no change. It would be a fair game. Warm up

HW: 3-61 through 3-66 3.1.5 Expected Value October 27, 2015

CO: SWBAT calculate the expected value. Objectives CO: SWBAT calculate the expected value. LO: SWBAT explain what expected value is and use mathematical vocabulary.

3-53. Examine the spinner at right 3-53.  Examine the spinner at right.  If the central angle of Region A is 7°, calculate the expected value of one spin using two different methods.  Be ready to share your methods with the class. 7 360 100 + 353 360 2 3.9 Or 7(100) + 353(2) 700 + 706 1406 1406 360 Teams

C: together a&b partners 3-54.  Now reverse the process.  For each spinner below, determine the value of x so that the expected value of the spinner is 3.  Be prepared to explain your method to the class. c. 1 4 𝑥 + 1 4 −3 + 40 360 18 + 140 360 9 =3 .25x + 4.75 = 3 .25x = -1.75 x = -7 a. 1 4 𝑥 + 3 4 2 =3 .25x + 1.5 = 3 .25x = 1.5 x = 6 b. 240 360 𝑥 + 60 360 −3 + 60 360 1 =3 240𝑥 360 + −180 360 + 60 360 =3 240x – 180 + 60 = 1080 240x – 120 = 1080 240x = 1200 x = 5 C: together a&b partners

3-51. BASKETBALL: Shooting One-and-One Free Throws Revisited 3-51.  BASKETBALL: Shooting One-and-One Free Throws Revisited. Recall the One-and-One situation from problem 3-26. In this problem, Dunkin’ Delilah Jones has a 60% free throw average. makes Use a model to represent the sample space.  What is the most likely of the three possible outcomes? 2 pts = 36%, 1 pt = 24%, 0 pts = 40% Is it more likely that Delilah would make no points or that she would score some points?  Explain. Some, she has a 60% chance of scoring points. On average, how many points would you expect Dunkin’ Delilah to make in a one-and-one free throw situation?  That is, what is the expected value? .36(2) + .24(1) + .4(0) = .96 Repeat part (a) for at least three other possible free throw percentages, making a note of the most likely outcome for each one. .6 makes .6 .4 misses .4 misses optional