1. 3-47.  TAKE A SPIN
Consider the following game: After you spin the wheel at right, you win the amount spun.
If you play the game 10 times, how much money would you expect to win?  What if you played the game 30 times?  100 times?  Explain your process.
5(0) + 5(4) = 20; 15(0) + 15(4) = 60; 50(0) + 50(4) = 200
If you were to play only once, what would you expect to earn according to your answers in part (a)?  Is it actually possible to win that amount?  Explain why or why not.
20/10 = $2, no because on one spin you can only get $4 or $0, nothing in between.

2. Expected Value
October 10, 2019
HW: 3-61 through 3-66

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

4. 3-48. What if the spinner looks like the one at right instead?
If you win the amount that comes up on each spin, how much would you expect to win after 4 spins?  What about after 100 spins?
(0) = $104; 25(4) + 25(100) + 50(0) = 2600
Calculate this spinner’s expected value.  That is, what are the expected winnings for each spin?  Be ready to justify your answer.
104/4 = $26 per spin
Gustavo described his thinking for part (b) this way: “Half the time, I’ll earn nothing.  One-fourth the time, I’ll earn $4, and the other one-fourth of the time I’ll earn $100.  So, for one spin, I can expect to win 1/2(0) +  1/4($4) +  1/4($100) .”  Calculate Gustavo’s expression.  Does his result match your result from part (b)?
Yes, $26
Hot Potato

5. 3-49. Jesse has created the spinner at right
3-49.  Jesse has created the spinner at right.  This time, if you land on a positive number, you win that amount of $. However, if you land on a negative number, you lose that amount of $!
Before analyzing the spinner, predict whether a person would win money or lose money after many spins.
Now calculate the actual expected value.  How does the result compare to your estimate from part (a)?
¼(6) + ¼(2) + 1/8(-2) + 3/8(-5) = -1/8 or -.125
What would the expected value be if this spinner were fair?  Discuss this with your team.  What does it mean for a spinner to be fair?
0; if the likelihood of winning or losing is exactly the same.
How could you change the spinner to make it fair?  Draw your new spinner and show why it is fair.
Teammates
Consult (a)

6. What does it mean if a dice or spinner has an expected value of 0?
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?
− =− 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.