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Probability question concerning odd makers and spread

  1. Oct 23, 2011 #1
    1. The problem statement, all variables and given/known data

    A bookie will pay you 6$ for every 1$ bet if you correctly select the winners (adjusted by a spread) in three games. What is the bookies expected earnings? (spread is how much the team wins by, and, when added to the underdog's score, should result in a tie)


    2. Relevant equations

    E[x]=sum(x*f(x))

    3. The attempt at a solution
    I'm having trouble getting started and making a probability density function for this because I don't really know how to deal with "the spread". If there was no spread would the pdf look like this?:
    X=number of winners selected........money earned by bookie.......probability
    0.................................................... $3.............................. 1/8
    1.................................................... $-3...............................3/8
    2................................................... $-9................................3/8
    3.....................................................$-15...............................1/8

    and then his expected earnings for this would be 3*(18)+(-3)*(3/8)+(-9)*(3/8)+(-15)*(1/8)
     
  2. jcsd
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