What is the probability of randomly selecting a three-child family with exactly two girl children?

2/6 is not accurate. using a theoretical method for equally likely outcomes, there are 2 possible outcomes for each birth: either a boy(B), or a girl (G). For a family of three children, the total number of possibilities (birth orders) is 2*2*2=8 to double check this work, here are the eight possible outcomes:

BBB, BBG, BGG, GBB, GBG, GGB, and GGG. You want EXACTLY two girls, this assumes that the other must be a boy. Therefore, the probability that a three child family has 2 girls one boy is P(2 girls)=3/8=0.375