Section 4.6 Mathematical Expectation and Odds

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Section 4.6Mathematical Expectation and Odds

• Warm up

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Mathematical Expectation

• It is the expected monetary value of an event.
• ME p()

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• Mulvihill is bidding on a landscaping job so he
  can make some money for senior week.
• The profit for the Alapocas job should be about
  3200 for the year with a probability of 0.87.
  The profit of the Hockessin job will be 3000
  with a probability of 0.91.
• However, with the costs of running the
  landscaping he will lose 700 on equipment
  repairs with a probability of 0.39.
• What is his expected return for each job?

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• Janavel made up a new game using one die.
• If someone rolls an even number, they win 2.
• If they roll a one, they win 5.
• If they roll a 3 or a 5, they pay 4.
• It costs 2 to play. What is the mathematical
  expectation?

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ODDS

• Odds in favor
• Formula p to q
• p want, q dont want
• Odds against
• Formula q to p
• p want, q dont want

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SHUT UP!

• The probability of Mrs. Godfrey telling the
  students to Shut it is 87.
• What are the odds in favor of her screaming Shut
  it?
• What are the odds against her screaming Shut it?

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World Series

• The Yankees have a ? chance of winning the the
  World Series.
• What are the odds in favor of them winning?
• What are the odds against them losing?

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Deal or No Deal

• In the Game Show Deal or No Deal, a contestant
  begins by choosing 1 of 26 numbered cases. Each
  case holds a different amount. Neither the host
  or the banker, who offers to buy the contestants
  case after each round, know what any case
  contains.

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• What is the probability that you choose the
  1,000,000 case to begin with?
• If you played the game many, many times, what is
  the expected value of the amount that your case
  contains?
• Worksheet

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Play as a Class

• Record the following information in the table.