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Math Help - Probability Probelms & Counting Techniques

  1. #1
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    Probability Probelms & Counting Techniques

    you guys have been such a big help lol. i have... i think just one maybe two more question that i need help with.

    You play a coin toss game with your friend. The game is that you toss three coins. If ALL heads or ALL tails come up, your friend pays you 4$. If any other combination appears, you pay your friend 1.50$

    a) show (using expectation) that this game is unfair.


    b) to whom is this game unfair?
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  2. #2
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    Quote Originally Posted by 16sammy View Post
    you guys have been such a big help lol. i have... i think just one maybe two more question that i need help with.

    You play a coin toss game with your friend. The game is that you toss three coins. If ALL heads or ALL tails come up, your friend pays you 4$. If any other combination appears, you pay your friend 1.50$

    a) show (using expectation) that this game is unfair.


    b) to whom is this game unfair?
    Pr(3 heads) + Pr(3 tails) = (1/2)^3 + (1/2)^3 = 1/4.

    Let X be the random variable amount of money won by you in a game.

    E(X) = (1/4)(4) + (3/4)(-1.5) = ......

    If the game is fair, E(X) = 0.

    If E(X) < 0, the game is unfair to you (why?)

    If E(X) > 0, the game is unfair to your friend (why?).
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  3. #3
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    The pmf is

    xi : p(xi)
    4 : .125
    -1.5 : .125
    -1.5 : .125
    -1.5 : .125
    -1.5 : .125
    -1.5 : .125
    -1.5 : .125
    4 : .125

    and so E(X) = x1p(x1)+...+x8p(x8) = -.125
    Last edited by Jacobsen; June 10th 2008 at 07:15 PM. Reason: i did it wrong
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  4. #4
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    well actually if the game is unfair it wont equal 0. the way u figure it out it will give u negative or positive number. if its negative its bad for u it its positive its good for u.

    that i know. im just not good at getting the math of it.
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  5. #5
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    Quote Originally Posted by 16sammy View Post
    well actually if the game is unfair it wont equal 0. the way u figure it out it will give u negative or positive number. if its negative its bad for u it its positive its good for u.

    that i know. im just not good at getting the math of it.
    So what in my reply do you not understand?
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  6. #6
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    sorry i misread one thing. but i cant just put e(x) <0... i have to have actual answers. so im assuming that if i punch that in my calc. it will give me answer lol...

    idk its just a little confusing...
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  7. #7
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    Quote Originally Posted by 16sammy View Post
    sorry i misread one thing. but i cant just put e(x) <0... i have to have actual answers.
    [snip]
    That would probably be why I wrote:

    E(X) = (1/4)(4) + (3/4)(-1.5) = ......

    in my very first reply.

    The ...... means that the final bit of arithmetic was left for you to do.

    I really don't see why this question is still causing you so much trouble.
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  8. #8
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    because i did that... and its not the right answer. i asked someone else and he was like... who ever told u that has no idea what hes talking about. he already did this nd got it right.
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  9. #9
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    Quote Originally Posted by 16sammy View Post
    because i did that... and its not the right answer. i asked someone else and he was like... who ever told u that has no idea what hes talking about. he already did this nd got it right.
    Did what? Got what answer? And what answer did this friend of yours get? Perhaps in the future you should just get help from this friend of yours since clearly I have no idea what I'm talking about ......
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    i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.
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  11. #11
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    Quote Originally Posted by 16sammy View Post
    i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.


    Here is my original reply:

    Quote Originally Posted by mr fantastic View Post
    Pr(3 heads) + Pr(3 tails) = (1/2)^3 + (1/2)^3 = 1/4.

    Let X be the random variable amount of money won by you in a game.

    E(X) = (1/4)(4) + (3/4)(-1.5) = ......

    If the game is fair, E(X) = 0.

    If E(X) < 0, the game is unfair to you (why?)

    If E(X) > 0, the game is unfair to your friend (why?).
    Just where did I say E(X) = 0?

    I said:

    E(X) = (1/4)(4) + (3/4)(-1.5) = ......

    Then I showed how the answer was to be interpreted:

    If the game is fair, E(X) = 0.

    If E(X) < 0, the game is unfair to you.

    If E(X) > 0, the game is unfair to your friend.




    NOTE: E(X) = (1/4)(4) + (3/4)(-1.5) = -1/8.

    Those bunch of fractions in the equation (as you so quaintly call them) are actually a necessary part of getting the final answer.


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  12. #12
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    Quote Originally Posted by 16sammy View Post
    i didn't say that did i? if i did im sorry i didnt mean it like that. i would get this friend to help but he wasnt online earlier. the answer isn't supposed to be 0.somethign cant remember. its a whole number. idk i havent gotten the answer yet he just told me how to do it. and it doesnt have a whole bunch of fractions in the equation.
    Since Mr Fantastic's reply is the correct answer to the question you have asked there are three possibilities:

    1. Your friend is wrong

    2. You have misunderstood your friends explanation

    3. You have posted the wrong question

    In all three cases we can do no more

    RonL
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