1. Expected values of games
You decide to buy a $2 Powerball ticket when you hear that the prize is $100,000,000. What is the expected value of this “game”?
Rules
Pick 5 “white” numbers out of 60 possible values. No numbers are repeated.
Pick one “red” number from 35 possible values.
5 correct
1 correct
4 correct
3 correct
0 correct
All others
$100,000,000
$200,000
$10,000
$100 $7 $4 $3
-$2

2. Discrete Math Section 16.6 Find the expected value of a game
In 100 spins the expected outcome is:
25($1) + 25($3) + 25 ($5) + 25 (-$10) = -$25
You could expect to lose $25 after having played 100 times
The values $1, $3, $5, and -$10 are called the payoff. -$25 is the expected value of the game

3. The expected value of a game is calculated by:
If the expected value is zero, the game is fair.
Expected value = x1 ∙ P(x1) + x2 ∙ P(x2) + … xn ∙ P(xn)

4. Example
Two coins are tossed. If both land heads up, then player A wins $4 from player B. If exactly one coin lands heads up, then player B wins $1 from A. If both land tails up, then B wins $2 from A. Is this a fair game?

5. Page 635 problem 19
Event
Bid accepted
Bid denied
Payoff
Probability

6. Assignment
Page 633
Problems 2,4,6,8,9,11,14,17,18,20,22,24