No. You've gained no useful information. The person who announces the gender of one child can say one of two things: "this child is a girl" or "this child is a

No. You've gained no useful information. The person who announces the gender of one child can say one of two things: "this child is a girl" or "this child is a boy." However, these two statements are symmetric in their effect on P(one child is a girl and one is a boy). There's a huge difference between announcing the gender of one child and announcing the gender of both children. If the announcer announces both children's genders, he can say that "both are boys," that "both are girls," or that "one is a boy and one is a girl." But the last statement is not symmetric to the first two in how it affects P(one child is a boy and one is a girl).