Correct Answer - D
Let event B is being boy while event G being girl. According to the question, `P(B)=P(G)=(1)/(2)`
Now , required conditional probability that all childeren are girls given that at least two are girls , is
`=("All 4 girls ")/( "(All 4 girls )+ (exactly 3 girls + 1 boy )+( exactly 2 girls + 2 boys )")`
`(((1)/(2))^(4))/(((1)/(2))^(4)+""^(4)C_(3)((1)/(2))^(3)((1)/(2))+""^(4)C_(2)((1)/(2))^(2)((1)/(2))^(2))=(1)/(1+4+6)=(1)/(11) `