A family having 4 children has 3 girl children. What is the probability that their 4th child is a son? This is similar to the two child problem.
So there are five cases, the gender of the children written according to their age,


*

*GGGG

*GGGB

*GGBG

*GBGG

*BGGG


So the probability should be $\frac{4}{5}$. But the given answer is $\frac{3}{4}$.
Am I missing something?
 A: The problem statement says that a family has 4 kids, and that 3 of them are girls. Because they don't say "at least" 3 of them are girls, we understand they what they actually mean is "exactly" 3 of them are girls and the remaining kid is a boy. What is the probability that the $4$th child is a boy?
By $4$th child they mean the youngest. So how are the genders distributed among ages? We can have either of the $4$:


*

*GGGB;

*GGBG;

*GBGG;

*BGGG;


where the leftmost is the older sibling and the rightmost is the younger one. Thus, out of those $4$ possible arrangements, only in one the youngest kid is a boy and thus the answer should be $\frac14$. $\frac34$ is the answer to "what is the probability that the 4th kid is a girl" or "what is the probability that the boy is not the 4th kid" or anything along those lines.
A: In a real life situation, it depends on how you know that the family has 3 girls. Here are two different scenarios:
A. You run into the mother with 3 of her children with her that are all girls, and she tells you that she has a 4th child. Now the chance of the 4th child being a boy is $\frac{1}{2}$
B. You are in a room with a bunch of parents, and someone asks: 'who is a parent of exactly 4 children, at least 3 of which are girls?', and the mother of this family raises her hand. Now the probability of her 4th child being a boy is $\frac{4}{5}$, following exactly your explanation.
There may be other scenarios yet, leading to different answers yet, and some might even lead to a probability of $\frac{3}{4}$, but I think scenarios isomorph to either one of these two cases are most likely to happen in real life. So I don't like the answer of the book either.
