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Math Help - probability of rolling a die

  1. #1
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    probability of rolling a die

    A casino game has the following rules: roll a fair six-sided die once. If you roll a 1, you get $12. If you roll a 3, you get $3. If you roll any other number, you lose $1.

    if u were running a casino, would u want this game there? why or why not?
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  2. #2
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    Quote Originally Posted by imverystupid View Post
    A casino game has the following rules: roll a fair six-sided die once. If you roll a 1, you get $12. If you roll a 3, you get $3. If you roll any other number, you lose $1.

    if u were running a casino, would u want this game there? why or why not?

    We should compute expected value, if the casino comes out positive, you would want the game

    So,

    P(rolling a 1) =\frac{1}{6}
    P(rolling a 3) =\frac{1}{6}
    P(rolling 2 or 4 or 5 or 6) =\frac{4}{6}

    Expected value=P(rolling a 1)*($ won by rolling a 1)+P(rolling a 3)*($ won by rolling a 3)+P(rolling 2 or 4 or 5 or 6)*($ won by rolling a 2 or 4 or 5 or 6)

    =\frac{1}{6}(12)+\frac{1}{6}(3)+\frac{4}{6}(-4)=2+.5-2-\frac{2}{3}=\frac{1}{2}-\frac{2}{3}


    This is a negative number. So if you play this game you will lose money over the long run. So a casino would be happy to have this game
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