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Section 13.4

Section 13.4. Expected Value. Objectives. Compute expected value. Use expected value to solve applied problems. Use expected value to determine the average payoff or loss in a game of chance. Key Terms.

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Section 13.4

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  1. Section 13.4 Expected Value

  2. Objectives • Compute expected value. • Use expected value to solve applied problems. • Use expected value to determine the average payoff or loss in a game of chance.

  3. 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.

  4. 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 EVto represent expected value.

  5. 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.

  6. Example 1:Calculating Expected Value • TB pg. 762/1

  7. Example 2:Calculating Expected Value • TB pg.763/3

  8. Example 3:Calculating Expected Value • TB pg.763/5

  9. Example 4:Calculating Expected Value • TB pg.763/7

  10. Example 5:Calculate Price to Make Game Fair • TB pg.763/9

  11. Example 6:Calculate Price to Make Game Fair • TB pg.763/11

  12. Example 7:Calculations • TB pg.763/13 • 1st Calculate EV, Determine Fair, Determine Fair Price

  13. Example 8:Calculations • TB pg.763/15 • 1st Calculate EV, Determine Fair, Determine Fair Price

  14. Example 9:Roulette Wheel • TB pg.763/17 • Calculate EV

  15. Example 10:Standardized Test • TB pg.763/21 • Guessing

  16. Example 11:Standardized Test • TB pg.764/23 • Guessing

  17. Example 12:Life Insurance • TB pg.764/25 • Calculate EV

  18. Example 13:Expected Gain/Loss • TB pg.764/29 • Calculate Gain/Loss

  19. Example 14:Expected Weekly Profit • TB pg.764/31 • Calculate Profit

  20. 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.

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