Wrong, wrong, WRONG. You DO NOT understand the problem, if you think that this means the probability of the other child being a boy is 1/2. GB and BG are equivalent linguistically, but not mathematically; they do not represent identical possibilities in the space of all conceptual representations of a family of two.

Here, I'll prove it for you:

    ;; Have a child, with an equal probability of the child being a boy or a
    ;; girl.
    (defun make-child ()
      (if (eql (random 2) 0)
          'boy
          'girl))

    ;; Make a family of n members, with each child having an equal probability
    ;; of being either a boy or a girl.
    (defun make-family (n)
      (do ((family nil)
           (i 0 (+ i 1)))
          ((>= i n) family)
        (push (make-child) family)))

    ;; As in the story, meet someone at a party who informs us that (1) she or
    ;; he has two children, and (2) that at least one of these children is a
    ;; girl.  E.g.,
    ;;
    ;; Me: "Hi there, what's your name?"
    ;; Cute lady: "Jennifer"
    ;; Me: "Nice to meet you, Jennifer, I'm Mark.  What brings you here?"
    ;; Jennifer: "Well my husband is out of town on a business trip, so I
    ;;            wanted to come here and catch up with some old friends of
    ;;            mine.  Fortunately I was able to get a baby sitter for my
    ;;            two kids on such short notice.  One of the kids, Meg, has
    ;;            to be up early in the morning for dance practice and..."
    ;; Me: "Husband?  Damn, all the good ones are taken."
    ;; Jennifer: "What?"
    ;; Me: "Nothing.  Hey, hang on while I work out the probability that your
    ;;      other child is a boy, based on the information that you've already
    ;;      given me."
    ;; Jennifer: "You're weird.  Have a good evening."
    ;;
    ;; This function works by calling (make-family 2) repeatedly until we get a
    ;; family that meets both of these criteria, then returns a representation
    ;; of said family.  This is a precise analogy for the story: just as the
    ;; fictional person at this party, here we take the space of all possible
    ;; conceptual representations of a family of two, then discard any of these
    ;; that *does not* include at least one female child.  THIS IS THE ONLY
    ;; REASONABLE WAY TO HANDLE THE INFORMATION THAT JENNIFER RELATES IN THE
    ;; ABOVE EXCHANGE.
    (defun meet-at-party ()
      (do ((family (make-family 2) (make-family 2)))
          ((find 'girl family) family)))

    ;; Perform the (meet-at-party) scenario num-total times, and then return
    ;; the fraction of those times in which the family contained a boy.
    (defun run-test (num-total)
      (let ((num-with-boys 0))
        (dotimes (i num-total (float (/ num-with-boys num-total)))
          (if (find 'boy (meet-at-party)) (incf num-with-boys)))))

Just call (run-test 1000000) or something. The result is approximately 2/3.