Question

There are two children in the family. one is a boy, then what is the probability that the other is a boy too?

Answer 1

50% Chance its a boy 
50 % Chance its a girl

Answer 2

One of them is a boy (but we don't know which one).
With two children there are 4 a priori possibilities (in order):
BB-BG-GB-GG, each with an equal chance of 14

The GG must be left out, because we know that one child is a boy.

There are two chances with a girl (BG and GB) out of a total of three leftover possibilities, so the chances are 23

Hope this helps!