Question 939002
  
It all looks confusing when we try to juggle with all those numbers in the head.  The problem can be solved systematically by constructing a contingency table.
  
role/gender B G total
speaking...... 4 4 8
silent............ 4 8 12
total............. 8 12 20

Probability of a child having a speaking part is therefore {{{(4+4)/20=8/20=2/5}}}