gistfile1.md

Initially, these four outcomes are equally probable:

older child   younger child
-----------   -------------
    boy            boy         P = 1/4
    boy            girl        P = 1/4
    girl           boy         P = 1/4
    girl           girl        P = 1/4

Now I tell you that one of the children is a boy:

older child   younger child
-----------   -------------
    boy            boy         P = 1/3
    boy            girl        P = 1/3
    girl           boy         P = 1/3

Note that if I identify which child is a boy, the probability is 1/2. For instance, suppose I tell you that one of the children is a boy, and it's the older of the two children. Then:

older child   younger child
-----------   -------------
    boy            boy         P = 1/2
    boy            girl        P = 1/2