In New York Park area, there are two Houses H1 and H2. Both H1 and H2 have two children each.

In House H1, The boy plays for New York Youth academy and the other child plays baseball.

In House H2, The boy Plays soccer for his school at New York and they recently have a newborn.

Can you prove that probability of House-H1 having girl child is more than that of House-H2?

In House H2, we know that older child is boy, therefore there are two cases

Older Younger

Boy Girl

Boy Boy

Probability of at least one girl child: 1/2

In House H1 there are three cases

Older Younger

Boy Girl

Boy Boy

Girl Boy

Probability of at least one girl child: 2/3