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March 29, 2017

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During a game, a balanced die is rolled. A player receives $22 when an even number is rolled, and loses $12 when an odd number is rolled. How much money can he expect on average in the long run?
Is the answer 17?

  • Math - ,

    For a balanced die, the probability of getting an even number is n({2,4,6})/n({1,2,3,4,5,6})=1/2.
    Similarly, the probability of getting an odd number is 1/2.
    Thus, the expected gain/roll is
    expected gain - expected loss
    = 0.5*$22 - 0.5*$12
    = $11-$6
    =$5 per roll on average in the long run

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