Probability: find the probability of event B given that event A occurs My Problem,
Suppose a family has 2 children,
if one children is randomly selected and it is a girl then what is the probability of the second child to be a girl ?
Please help. Thanks

"if one children is randomly selected and it is a girl then what is the probability of the second child to be a girl"
This is one of the worst cases of ambiguity in a question that I've seen in a while.  "second child" usually means the one born after the first child, but that seems to conflict with the statement that one of the two is randomly chosen.  I have to construe "the second child" to mean "the other child".
$$
\begin{array}{ccl}
\text{first born} & \text{second born} \\
\hline
\text{boy} & \text{boy} & \longleftarrow\text{This case is ruled out.} \\
\text{boy} & \text{girl} \\
\text{girl} & \text{boy} \\
\text{girl} & \text{girl}
\end{array}
$$
If one of two randomly chosen is a girl, then in one of the three cases not ruled out, the other one is a girl.  So $1/3$ is the bottom line.
