A college student was chatting with his statistics professor. She said, "I have two children, the older one of whom is a girl."
What is the chance that the professor's children are both girls?
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Let the older child be the first letter, and B = boy, G = girl.
The four possibilities are: BB, BG, GB, GG.
Since the oldest child is a girl, that eliminates BB and BG. Of the two remaining possibilities, one has both children as girls.