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:

Correct option is A. 1/11
Let B denote boy and G denote girl
P(B)=P(G)=1/2
Required Probability = P(all 4 girls | at least 2 girls)
= P(all 4 girls) / P(at least 2 girls)
= P(all 4 girls) / [P(all 4 girls) + P(exactly 3 girls + 1 boy) + P(exactly 2 girls + 2 boys)]
= (1/2)^4 / [(1/2)^4 + 4C3(1/2)^4 + 4C2(1/2)^4]
= (1/16) / [(1/16) + (4/16) + (6/16)]
= (1/16) / (11/16)
= 1/11