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Math Help - Probability Distribution Question

  1. #1
    Junior Member asemh's Avatar
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    Probability Distribution Question

    Hi

    Im having this problem with a Probability Distribution question.. I just don't seem to know how to do this.

    So here's the question:

    A spinner with five regions is used in a game. The probabilities of the regions are...

    P(1) = 0.3
    P(2) = 0.2
    P(3) = 0.1
    P(4) = 0.1
    P(5) = 0.3

    The rules of the game are as follows: If you spin and land on an even number, you receive double that number of points. If you land on an odd number, you lose that number of points. What is the expected number of points a player will win or lose.

    I did find the expected number and my answer was right.. but then question e) confused me...

    e) alter the game to make it fair. Prove mathematically that your version is fair.


    In the other questions i had to do probability distributions and stuff and for the expected value i got a number other than 0 (basically its an unfair game). But I am really confused as how to alter this game so that the expected number is zero and it is fair.

    Thanks in advance
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  2. #2
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    Here is a hint- sum up the expected values of the evens and subtract the sum of the expected values for odds from it. Set that expression equal to 0, and solve so that evens == odds.
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  3. #3
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    Quote Originally Posted by asemh View Post
    Hi

    Im having this problem with a Probability Distribution question.. I just don't seem to know how to do this.

    So here's the question:

    A spinner with five regions is used in a game. The probabilities of the regions are...

    P(1) = 0.3
    P(2) = 0.2
    P(3) = 0.1
    P(4) = 0.1
    P(5) = 0.3

    The rules of the game are as follows: If you spin and land on an even number, you receive double that number of points. If you land on an odd number, you lose that number of points. What is the expected number of points a player will win or lose.

    I did find the expected number and my answer was right.. but then question e) confused me...

    e) alter the game to make it fair. Prove mathematically that your version is fair.


    In the other questions i had to do probability distributions and stuff and for the expected value i got a number other than 0 (basically its an unfair game). But I am really confused as how to alter this game so that the expected number is zero and it is fair.

    Thanks in advance
    Let's say that if you land on an odd number, you lose that number of points, but if you land on an even number, you win x times the number of points, where x is some number yet to be determined.

    Is there a value of x that makes the game fair?
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