Section 13.4

Expected Value

Objectives1. Compute expected value.

2. Use expected value to solve applied problems.

3. Use expected value to determine the average payoff or loss in a game of chance.

Key Terms Expected Value: a mathematical way to use

probabilities to determine what to expect in various situation over the long run.• Used to determine premiums on insurance policies, weigh

the risks versus the benefits of alternatives in business ventures, and indicate to a player of any game of chance what will happen if the game is played repeatedly.

Expected Value: The standard way to find expected

value is to multiply each possible outcome by its probability, and then add these products.• We will use EV to represent expected

value.

Key Concept: Determining if a game is fair:

• If a game has an expected value of 0, then the game is called fair.• A game in which the expected value is not 0 is

an unfair game.

Example 1:Calculating Expected Value

TB pg. 762/1

Example 2:Calculating Expected Value

TB pg.763/3

1 2 3 4 5 6123456

Example 3:Calculating Expected Value

TB pg.763/5

Example 4:Calculating Expected Value

TB pg.763/7

Example 5:Calculate Price to Make Game Fair

TB pg.763/9

Example 6:Calculate Price to Make Game Fair

TB pg.763/11

Example 7:Calculations

TB pg.763/13• 1st Calculate EV, Determine Fair, Determine Fair Price

Example 8:Calculations

TB pg.763/15• 1st Calculate EV, Determine Fair, Determine Fair Price

Example 9:Roulette Wheel

TB pg.763/17• Calculate EV

Example 10:Standardized Test

TB pg.763/21• Guessing

Example 11:Standardized Test

TB pg.764/23• Guessing

Example 12:Life Insurance

TB pg.764/25• Calculate EV

Example 13:Expected Gain/Loss

TB pg.764/29• Calculate Gain/Loss

Example 14:Expected Weekly Profit

TB pg.764/31• Calculate Profit

Section 13.4 Assignment Class work:

• TB pg. 763/2 – 32 Even• Remember you must write problems and show ALL work to receive credit for this assignment.• Class assignments are 40% of your grade.

• This assignment is due Friday, 12/02/11.