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Math Help - Expected Gain?

  1. #1
    Junior Member Kaloda's Avatar
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    Expected Gain?

    John played a game where he has to pick one stone in a box that contains 38 stones each labeled from 1 to 38. Suppose that he bet $100 that he'll pick a stone numbered 1-9. Suppose also that the host will triple his bet if he wins. What is JOhn's expected net winnings?
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Expected Gain?

    I assume that what you mean is that if he wins the bet he makes $300 and if he loses he is out $100.

    The expected value of his winnings is the probability of each outcome times its outcome. In this case there is a 9/38 change of winning $300, and (38-9)/38 = 29/38 change of losing $100. So the expected outcome is:

    (9/38)($300) + (29/38)(-$100) = $71.05 - $76.32 = -$5.26
    Last edited by ebaines; November 13th 2013 at 12:56 PM.
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  3. #3
    Junior Member Kaloda's Avatar
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    Re: Expected Gain?

    Quote Originally Posted by ebaines View Post
    I assume that what you mean is that if he wins the bet he makes $300 and if he loses he is out $100.

    The expected value of his winnings is the probability of each outcome times its outcome. In this case there is a 9/38 change of winning $300, and (38-9)/38 = 27/38 change of losing $100. So the expected outcome is:

    (9/38)($300) + (27/38)(-$100) = $0.

    In other words he should expeect to come out even.
    38-39=29, not 27.

    And also, I have the same solution as yours, but I'm confused if I must use (300-100) or $200 instead of $300.
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  4. #4
    Junior Member Kaloda's Avatar
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    Re: Expected Gain?

    I thought he'll win $300 less $100 for his bet thus totaling to $200. Am I wrong?
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  5. #5
    MHF Contributor ebaines's Avatar
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    Re: Expected Gain?

    I realized the error and fixed it right after posting - it seems my correction occurred just a minute before your posting.

    The wording of the problem is unclear. I've never heard the phrase "the host will triple his bet" before, so I'm not really sure what it's intended to mean. I'm guessing that it means "the house will pay off triple his bet," so he gets his original bet back plus three times that amount. But to be honest - only the person who wrote this problem knows what it means for sure.
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    Re: Expected Gain?

    Quote Originally Posted by ebaines View Post
    I realized the error and fixed it right after posting - it seems my correction occurred just a minute before your posting.
    The wording of the problem is unclear. I've never heard the phrase "the host will triple his bet" before, so I'm not really sure what it's intended to mean. I'm guessing that it means "the house will pay off triple his bet," so he gets his original bet back plus three times that amount. But to be honest - only the person who wrote this problem knows what it means for sure.
    All of that is certainly true.
    However, is most gaming houses one pays to play.
    In this case I would expect to pay $100 to play.
    If I won the house pays me $300 and nothing if I lose.
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