Two Children 1

$\frac{1}{3}$31​

When you first find out that your colleague has 2 children, the possibilities made known to you are:

1. Both children are boys
2. The older child is a boy, and the younger child is a girl
3. The older child is a girl, and the younger child is a boy
4. Both children are girls

Each outcome comes at equal chance.

However, when he reveals that at least one of them is a girl, then you can eliminate the first possibility. That leaves 3 possibilities, each with equal chance. Thus, the chances of him having 2 daughters is $\frac{1}{3}$31​.