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Finding expected Value

  1. Apr 8, 2005 #1
    The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one.

    $5900(1 chance in 8100); $2500( 1 chance in 6200); $600 (1 chance in 4700); $300(1 chance in 2600)
    Find the expected value of the amount won for one entry if the cost to enter is
    75 cents.

    Now I am having trouble setting this up as a probability distribution. I just don't know where to start or what goes where. I know the awnser is $0.62..but i just can't figure out the steps. So far i'v been doing it like this

    x P(x)
    ----- ------
    Win $5899.25 ?
    Lose -$.75 ?

    Well I think i'm setting up "x" wrong and I just don't know what the probability should be. So any help would be apreciated.
     
  2. jcsd
  3. Apr 8, 2005 #2
    For example, 1 chance in 100 is a probability.
    So you have the probability of every winning and the amount of each winning. Now, the expected value is

    [tex]E\left[ X \right] = \sum\limits_{i = 1}^n {X_i P\left( {X_i } \right)}[/tex]

    [tex]X_i[/tex] is the amount of each winning and [tex]P\left( {X_i } \right)[/tex] is the probability of each winning.
    And don't forget to take into account the 75 cents the entry consts.
     
  4. Apr 8, 2005 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    "One chance in 8100" means the probability is 1/8100, "one change in 6200" mean the probability is 1/6200, etc.
     
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