Probability and statistics

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A dice game involves rolling 2 dice. If you roll a 2, 3, 4, 10, 11, or a 12 you win $5. If you roll a 5, 6, 7, 8, or 9 you lose $5. Find the expected value you win (or lose) per game.

  • Probability and statistics -

    Prob(2) = 1/36
    prob(3) = 2/36
    prob(4) = 3/36
    prob(12) = 1/36
    prob(11) = 2/36
    prob(10) = 3/36
    total of above , your cases of winning = 12/36

    so the prob of remaining cases = 24/36

    expected value of game
    = (12/36)(5) + (24/36)(-5)
    = (1/3)(5) - (2/3)(5
    = -5/3

    You would be expected to lose $1.67

  • Probability and statistics -

    Prob(2) = 1/36
    prob(3) = 2/36
    prob(4) = 3/36
    prob(12) = 1/36
    prob(11) = 2/36
    prob(10) = 3/36
    total of above , your cases of winning = 12/36

    so the prob of remaining cases = 24/36

    expected value of game
    = (12/36)(5) + (24/36)(-5)
    = (1/3)(5) - (2/3)(5
    = -5/3

    You would be expected to lose $1.67

  • Probability and statistics -

    $1.67

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