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Math Help - Probability question (boys & girls)

  1. #1
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    Probability question (boys & girls)

    Hi, I'm new to this site. Sorry I'm jumping in with a question as the first post!

    There was a question in my textbook that goes like this:
    "A family has 2 kids. Given that at least one of them is a boy, what is the probability that both of them are boys?"

    My idea was this:
    Initially the kids could satisfy one of three cases:
    boy/boy, boy/girl, girl/girl
    But now that we are given that at least one of them is a boy, we can eliminate the case girl/girl. Out of the two remaining cases, one is favorable, so the probability should be 1/2.

    But the answer as given in the book is 1/3. What am I doing wrong?

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by whitehat View Post
    Hi, I'm new to this site. Sorry I'm jumping in with a question as the first post!

    There was a question in my textbook that goes like this:
    "A family has 2 kids. Given that at least one of them is a boy, what is the probability that both of them are boys?"

    My idea was this:
    Initially the kids could satisfy one of three cases:
    boy/boy, boy/girl, girl/girl Mr F says: You've missed an 'outcome': girl/boy. See below.

    But now that we are given that at least one of them is a boy, we can eliminate the case girl/girl. Out of the two remaining cases, one is favorable, so the probability should be 1/2.

    But the answer as given in the book is 1/3. What am I doing wrong?

    Thanks in advance.
    You're given that at least one is a boy. So the reduced sample space is:

    BG
    GB
    BB

    where the younger sibling is given first.

    So the probability that both are boys is 1/3.
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  3. #3
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    Thanks

    Oh... I didn't consider them as two separate entities. Thanks!
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