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Math Help - expected value of marbles

  1. #1
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    expected value of marbles

    question:

    We have 20 marbles in a bag, some red, some blue. We play the following game. We randomly pull a marble. If it is blue, we receive $10. Otherwise we pay $3. How many blue marbles are in the bag if we have an expected value of -$1.05 when playing this game?


    I'm not asking for the answer, just some guidance on how to get it.
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  2. #2
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    Hello, graffitihead!

    We have 20 marbles in a bag, some red, some blue.
    We randomly drawl a marble.
    If it is blue, we receive $10. Otherwise we pay $3.
    How many blue marbles are in the bag if we have an expected value of -$1.05?

    Let B = number of blue marbles in the bag.
    Then 20 - B = number of red marbles in the bag.

    We have: . \begin{array}{c|c|c|}<br />
& \text{Prob.} & \text{Payoff} \\ \hline \hline \\[-4mm]<br />
\text{Blue} & \frac{B}{20} & +\$10 \\ \\[-4mm] \hline \\[-4mm]<br />
\text{Red} & \frac{20-B}{20} & \text{-}\$3 \\ [-4mm] \\ \hline \end{array}


    The expected value is -$1.05

    . . \left(\tfrac{B}{20}\right)(+10) + \left(\tfrac{20-B}{20}\right)(\text{-}3) \;=\;\text{-}1.05


    And solve for B . . .

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