If a couple plans to have 9 children, what is the probability that there will be at least one girl? assume boys and girls are equally likely. is that probability high enough for the couple to be very confident that they will get at least one girl in 9 children?

Second question: maybe but nothing is certain when you're talking about anything between men and women. This is not part of the answer. It's just an observation.

Figure this question out first as though you don't get any females. They are all males. The total number of ways that you can distribute 9 children by gender is 2^9 = 512
There is only one way that you can get all males and that is M M M M M M M M M  so the chances are 1 chance in 512 or 1/512 
All males = 0.001953

So the chances of there being at least 1 female is
1 - 1/512 = 0.998

Which contrary to my opening remark is almost certainty.