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Math Help - Proving independence in probability

  1. #1
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    Proving independence in probability

    Hi, the question involves 3 parts.

    1.) A family has 3 children. Event A= at least 1 girl, B= children of both genders. Show that A and B. are independent.

    2.) If there are 2 children, use A, and B to show they are NOT dependent

    3.) If there are 4 children use A, and B to proven they are NOT independent

    It's mostly 3 that I'm not sure about, I've uploaded photos of my work

    Thank you
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  2. #2
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    Re: Proving indepencece in probabibility

    Proving independence in probability-image.jpg

    Proving independence in probability-image.jpg
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  3. #3
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    Re: Proving indepencece in probabibility

    Quote Originally Posted by crownvicman View Post
    Hi, the question involves 3 parts.

    1.) A family has 3 children. Event A= at least 1 girl, B= children of both genders. Show that A and B. are independent.

    2.) If there are 2 children, use A, and B to show they are NOT dependent

    3.) If there are 4 children use A, and B to proven they are NOT independent

    It's mostly 3 that I'm not sure about, I've uploaded photos of my work

    Thank you
    You don't care about the order of the genders at all so there is no reason to distinguish between say bgb and bbg. So your population is given by {bbb,bbg,bgg,ggg}.

    Assuming P(b)=P(g)=1/2. Your distribution is

    Pr[{bbb,bbg,bgg,ggg}] = {1/8, 3/8, 3/8, 1/8}

    Now A is {at least 1 girl} not {at most one girl} as you've written.

    So Pr[A] = Pr[bbg]+Pr[bgg]+Pr[ggg] = 7/8 not 1/2 as it looks like you've calculated.

    Pr[B] = Pr[bbg]+Pr[bgg] = 3/4

    Go back and rework things. I think you have the general idea.
    Thanks from mash
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  4. #4
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    Re: Proving indepencece in probabibility

    Thank you, I thought that all possibilities had to be included though? Wouldn't the varying possibility for each child's gender have to be taken into account?
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  5. #5
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    Re: Proving indepencece in probabibility

    I don't see anything in the problem that requires you to consider anything but the total number of boys and girls.
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  6. #6
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    Re: Proving independence in probability

    Quote Originally Posted by crownvicman View Post
    Hi, the question involves 3 parts.

    1.) A family has 3 children. Event A= at least 1 girl, B= children of both genders. Show that A and B. are independent.

    2.) If there are 2 children, use A, and B to show they are NOT dependent

    3.) If there are 4 children use A, and B to proven they are NOT independent

    It's mostly 3 that I'm not sure about, I've uploaded photos of my work

    Thank you
    You just wrote that Event A is "at least 1 girl". In your work, you wrote that Event A is "at most 1 girl". Which is it? (This was also asked by romsek, but still not answered).
    Last edited by SlipEternal; March 18th 2014 at 10:28 AM.
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