>while you would be left with 2/n - 1/(n^2) of BB

For those like me who didn't immediately understand where this came from:

    P(atleast one of two boys satisfies the condition)
    = 1 - P(neither of two boys satisfies the condition)
    = 1 - [P(a boy doesn't satisfy the condition)]^2
    = 1 - [1 - P(a boy satisfies the condition)]^2
    = 1 - [1 - 1/n]^2
    = 2/n - 1/n^2