Error in the problem solution. In the family in total will be 8 people including parents. Assuming one parent is male and another is female, we get update on the proportion of boys:girls among that family's childrens, because overall weighted proportion (including 1:1 for parents and some x:y for children) should match 1.09:1. So basically x:y proportion for children should be changed and we should get another answer (different from correct one in the submission).

I'm getting .696 which is not accepted.

20 * (109/209) ^ 3 * (1-(109/209))^3 + 15 * (109/209) ^ 4 * (1-(109/209))^2 + 6 * (109/209) ^ 5 * (1-(109/209))^1 + 1 * (109/209) ^ 6 * (1-(109/209))^0

What am I doing wrong?

Keep in mind that your answer is supposed to have exactly 3 digits after decimal point and be rounded away from zero. This is not clarified in the problem's description.

And where is Python 3 ?!

I am getting the wrong answer but i think i am doing in right way. Can anybody help me or tell me the correct answer

My R code is

dbinom(3, size=6, prob=109/209)+dbinom(4, size=6, prob=109/209)+dbinom(5, size=5, prob=109/209)+dbinom(6, size=6, prob=109/209)

and my answer is

0.6235209