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You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

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2 answers
  1. Given prob of not rolling 8 is 9/10
    then prob of rolling 8 = 1/10

    NOTE: with a roll of 2 fair dice, the above given probability is not correct,
    prob(rolling an 8) is 5/36 and prob (not rolling a sum of 8 is 31/36

    But, going with your data anyway, ....

    expected value = (1/10)(9) - (9/10)(1) = 0

    REAl expected value
    = (5/36)(9) - (31/36)(1) = 19/9 or appr 2.11

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  2. actually it is 1.25-.86

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