Question

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 A. `(1)/(17)` B. `(1)/(12)` C. `(1)/(10)` D. `(1)/(11)` Select the correct answer from above options

Answer 1

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) `