Yes, only one of these three families has 2 girls, while two of them have a boy and a girl. But they're not equally likely to be chosen. If you choose Ann or Courtney, then you have the family with two sisters. If you choose Heidi or Emily, you have a family with a brother and sister. You're twice as likely to choose the girl-girl family, which offsets having only half as many girl-girl families.
You're not choosing the individual kids, you're choosing the family. Your choices are family A (Ann and Courtney), family B (Heidi and Bradley), or family C (Gary, Emily).
You're choosing Ann's family, Courtney's family, Heidi's family, or Emily's family. We don't care about Bradley's or Gary's families. While there are only three families, one of those families is twice as likely to be chosen than the other two.
Based on the original question, you are choosing a family that has at least one girl. Ann's family is not considered a separate choice from Courtney's family.
This. 1/3.
Also because I know my mathematics and this is a standard learn to count/don't trust your gut for probability exercise.