1. In games of chance the expectations can be thought of as the average outcome if the game was repeated multiple times. Expectation These calculated expectations let us know if the game if fair. Final Expectation = (-) = You Lose! Final Expectation = 0 = Game is Fair Final Expectation = (+) = You Win!

2. Example: A lottery has a game where people can chose a three digit number from 000 to 999 for a 2$ cost. If those three numbers are selected that person wins $1000. Is this game fair? OutcomeMoney GainedProbabilityProduct Win (match all 3 #s) $ 9981 / 10000.998 Lose $ -2999 / 1000-1.998 Expectation = -1.000

3. €2 €8 €14 €4 Fair or Not Fair? Outcome (x)24814 Probability P(x)1/21/41/8 x ∙ P(x)1111.75 Expected E (x) = 4.75 – 5 = -0.25 Not Fair

4. You win the number that appears on the die in €uro €4 for a 4 €6 for a 6 etc A fun Fair game is called Numbers Up! You pay €4 to play and involves rolling a single die. Here are the rules: Fair or Not Fair?

5. A fun Fair game is called Numbers Up! You pay €4 to play and involves rolling a single die. Here are the rules: Fair or Not Fair? Outcome (x)123456 Probability P(x) 1/6 x ∙ P(x) 1/61/31/22/35/61 Expected E (x) = 3.5 – 4 = -0.5 Not Fair