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Math Help - Struggling with Assignment question

  1. #1
    Junior Member
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    Question Struggling with Assignment question

    This is the question exactly
    Alice: Let's take turns flipping a coin. The fi rst person who gets heads wins. I'll
    go fi rst.
    Bob: But you might win on the very fi rst throw. Let's compensate by giving me
    one extra throw on my first turn.
    Alice: Fine.
    Bob: And let's use my coin, which comes up heads with probability 'pi' .
    Alice: Well, then I had better know 'pi' before I agree.
    What value of 'pi' makes the game fair to each player?

    I have been stuck on this same problem for so long its embarrassing. I am not asking for the answer I just need someone to point me in the right direction. I thought I was supposed to work out the probability for each player winning in terms of pi assume they are equal, then solve for pi. I went through all my lecture notes and still nothing came to me. Please help!
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  2. #2
    MHF Contributor
    Joined
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    Re: Struggling with Assignment question

    i haven't worked it through but i would approach the problem like this:

    what is the probability of alice winning on turn 1?
    what is the probability of the game reaching turn 3 and alice winning on that turn 3?
    what is the probability of the game reaching turn 5 and alice winning on that turn 5?
    what is the probability of the game reaching turn 7 and alice winning on that turn 7?
    ....


    hence what is the probability of alice winning?

    find the value of pi that makes this 0.5.
    Last edited by SpringFan25; March 22nd 2012 at 02:18 PM.
    Thanks from stripe501
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