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Math Help - probability + 'fair'

  1. #1
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    probability + 'fair'

    I am having trouble with this one, specifically what the question is asking fair and the term 'fair', I have read through my notes and havent come across it. Just not sure what I'm supposed to solve here

    Two siblings are fighting over who gets to sit in the front seat during the drive to the movies. To resolve the fight, the mother gives them a coin and says “Ashley, flip this coin”. Then after seeing the result says, “Okay, now it’s your turn to flip the coin Jesse. If it lands differently than it did for Ashley, you get the front seat”.

    (a) If the coin is balanced (ie.
    P(Heads) = 1/2 ), is this a fair way to decide who sits in the front seat? explain

    (b) Suppose the coin is not balanced, and lands on Heads
    3/4 of the time. Is this method still fair? If not, which child is more likely to end up in the front seat?

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  2. #2
    MHF Contributor
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    "Fair" could mean a couple of things:

    1) Most likely, "fair" means that each player has an equal opportunity. None has any advantage over the other.

    2) It may mean "just". In this case, if you sign an agreement to take on a 1/4 probability of winning, then your 1:3 odds would be considered "fair", since you agreed to the terms.

    The coin flippers.

    #1 gets heads or tails, each with probability 1/2
    #2 gets heads or tails, each with probability 1/2

    Only four outcomes:

    HH - 1/4 - Same
    HT - 1/4 - Different
    TH - 1/4 - Different
    TT - 1/4 - Same

    It looks fair to me.

    You decide the other one.
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