A family has three children. What is the probability that at least one of them is a boy? According to me there are $4$ possible outcomes:

$$GGG \ \ 
BBB \ \ 
BGG \ \
BBG $$

Out of these four outcomes, $3$ are favorable. So the probability should be $\frac{3}{4}$.

But should you take into account the order of their birth? Because in that case it would be $\frac{7}{8}$!
The complement of at least one boy is all three girls

So, $P($ at least one boy$)=1-P(GGG)$

$=\displaystyle1-\left(\frac12\right)^3$

This is the de facto way of solving problems of Probability of at least one in case of Binomial Distribution like tossing a coin etc.
The possibilities are

ggg ggb gbg bgg gbb bgb bbg bbb 

at least one boy... 7/8