I have two children and a son who was born on a Thursday. What is the probability that I have a daughter? Let's denote the days of the week with the numbers $$1, 2, ... , 7$$ with $$1\ =$$ Monday, $$2 =$$ Tuesday and so on. Now we can define the event as "a boy was born on day $$n$$ " as $$B_n$$, and similarly for $$G_n$$.
For example, $$B_3$$ means a boy born on a Wednesday and $$G_1$$ means a girl born on a Monday. With this notation, we can write events like: $$B_3G_1$$ means: "The first child was a boy born on a Wednesday and the second child was a girl born on a Monday".
Let's assume that the probability of a child being born on each day of the week is the same (which, like the sex of the child, is not entirely true, but is a reasonable assumption to keep the problem simple). This leads to the following $$27$$ equally likely ways my children could have been born($$B_4$$ represents a boy born on Thursday):
$$\begin{matrix} B_4G_1 & G_1B_4 & B_1B_4 & B_4B_1\\ B_4G_2 & G_2B_4 & B_2B_4 & B_4B_2\\ B_4G_3 & G_3B_4 & B_3B_4 & B_4B_3\\ B_4G_4 & G_4B_4 & B_4B_4 & \\ B_4G_5 & G_5B_4 & B_5B_4 & B_4B_5\\ B_4G_6 & G_4B_4 & B_6B_4 & B_4B_6\\ B_4G_7 & G_7B_4 & B_7B_4 & B_4B_7 \end{matrix}$$
The table above is a complete list of all the ways in which two children can be born if at least one of them is a boy born on a Thursday. Under our assumptions, of course, all these events are equally likely. There are $$27$$ possibilities from which $$14$$ (those in the first two columns) contain a girl, so the probability that I have a daughter is $$14/27\approx 51.9\% \neq 50\%$$.