I wonder if it's possible you mis-stated the problem? If you tell me they have two children and that at least one is a daughter, the tested condition ("both children are girls") comes down to the other child also being a girl, with a probability of 50%. If the other child is a boy, then the condition is not true, and if the other child is a girl, the condition is true. The condition will be true in 50% of the cases. Am I missing something?
Put another way, "In all families with exactly two children, both children will be girls in 50% of families who have at least one girl."
I'm assuming, as you stated, that any given child has an equal chance of being a boy or a girl.
It's good to inform people who don't understand statistics. On the flipside, here are two points for people unfamiliar with security:
1. A broad screening for "terrorists" is not made with the expectation that every person flagged is a terrorist. Rather, it identifies behaviors that make a person worth giving a second look. If properly conducted, the flagged person is not treated or considered a threat during the second or even the third look. The 300 people you mentioned would almost certainly be treated politely and sent on their way (I myself have received a second or third look several times. No problem.)
2. Perhaps the most important purpose of a broad security screening is to discourage criminals from using that avenue in the first place. If I have several dozen potential means of attack, for example, the ones that involve getting a weapon onto an airplane are going to be near the bottom of the list. Not because I can't do it, but because, why bother?
One man's constant is another man's variable. -- A.J. Perlis