Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls , is

Options

A. `(1)/(17)`
B. `(1)/(12)`
C. `(1)/(10)`
D. `(1)/(11)`

Answer

D

Explanation

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) `