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Thread: boy/girl problem

  1. #1 boy/girl problem 
    Forum Professor
    Join Date
    May 2005
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    This is a pretty standard problem in introductory statistics classes, so if you’ve taken such a class and have seen it before please give others a chance to try to answer before posting the correct answer.

    If a couple has two children and one of the children is a boy, what are the odds that the other child is a girl?

    For the sake of simplicity let’s ignore biological arguments and assume that for any given birth having a boy or girl is equally likely.


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  3. #2  
    Forum Professor river_rat's Avatar
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    Spoiler (for those to lazy to take the 5 minutes to work it out) :

    The probability of the other child being a girl is 1/3. To see why look at the four ways you can have to children

    1. Older Girl + younger Girl
    2. Older Girl + younger Boy
    3. Older Boy + younger Girl
    4. Older Boy + younger Boy


    Given the data there is only one way out of three possibilities to have a girl in the family.


    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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