If a couple has 3 girls, what is the probability that their 4th child is a son? As a child is boy or girl; this doesn't depend on it's elder siblings.
So the answer must be 1/2, but I found that the answer is 3/4. What's wrong with my reasoning? Here in the question it is not stated that the couple has exactly 4 children
 A: As a (possibly irrelevant) remark:  I can give an interpretation which yields $\frac 15$.  This would be the case if we applied Laplace's rule of Succession.  That is, assuming we know that $G,B$ are both possible, we assume independence, we observe $GGG$ for the first three, but do not assume that the probability for each birth is $\frac 12$.  Rather we assume that the probability, $p$, is chosen uniformly at random (but is the same for each birth). 
Of course, as the comments show, there are other sensible interpretations which yield $\frac 12$, or $\frac 45$.  I haven't come up with one that yields $\frac 34$ but perhaps I lack imagination.  Worth noting that the solutions which give $\frac 12$ or $\frac 45$ both assume that there are exactly $4$ kids. If you don't want to make that assumption...well, then you need to make some other assumption about the meaning of the question or you can just fall back on Laplace (really a last resort, I'd have thought).
The main point here is that phrasing and interpretation are critical.  If the text presents the problem without clarification then I'd say the reader was obliged to go through the various sensible readings and either answer several of them or, at a minimum, clearly indicate what assumptions they are declaring.
