1. Quiz Time! Clear your desk except for a pencil & calculator!

3. Would you play this game? You flip a coin and you win $4 for heads, and lose $2 for tails. How could we predict what you would win on average if you played this game multiple times?

4. Another way to write this: OutcomesHeadsTails Probability½½ Value4-2 Total½(4)½(-2) 1 ½(4) + ½(-2) = 1

5. Expected Value Since you’d win $1 on average, it’s the value you could “expect” to win after playing over and over Expected Value: The value is what the player can expect to win or lose if they were to play a game many times.

6. Example 1 A die is rolled. You receive $1 for each dot that shows. What is the expected value for the game? Outcomes123456 Probability Value Total

7. Example 2 A $20 bill, two $10 bills, three $5 bills and four $1 bills are placed in a bag. If a bill is chosen at random, what is the expected value for the amount chosen? Outcomes Probability Value Total

8. Example 3 In a game, you flip a coin twice, and record the number of heads that occur. You get 10 points for 2 heads, 5 points for 1 head, and lose 2 points for no heads. What is the expected value for the number of points you’ll win per turn? (Hint: List every outcome.)

9. Your Turn! Find the expected value (or expectation) of the games described. 4) Mike wins $2 if a coin toss shows heads and $1 if it shows tails. 5) Jane wins $10 if a die roll shows a six, and she loses $1 otherwise. 6) A coin is tossed twice. Albert wins $2 for each heads and must pay $1 for each tails.

10. Mike wins $2 if a coin toss shows heads and $1 if it shows tails – $1.50 Jane wins $10 if a die roll shows a six, and she loses $1 otherwise – $0.83 A coin is tossed twice. Albert wins $2 for each heads and must pay $1 for each tails. – $1.00 Example 4: Solutions

11. Coming up… -Expected Value HW tonight - Office Hours Monday (for tutoring or to work on your project!) -Carnival Project due Tuesday! -Unit 2 Test Thursday!