Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
 (i) the youngest is a girl, (ii) at least one is a girl?

Explanation

Let AB and AC are two equal chords of the circle with centre at O . Let us join A, O and let it be produced to D.
We have to prove that AD passes through O , i.e., it is sufficient to prove that AD is the bisector of ` angle BAC` .
Construction : Let us join O , B and O,C .
Proof : In `Delta AOB` OB = OC (radii of same circle ) AB = AC (given) and OA is common to both.
`therefore Delta AOB ~ = Delta AOC` [ by the condition of S- S- S congruence of triangles ].
`therefore angle OAB = angle OAC [ because ` similar angles of congruent triangles ].
`therefore AO` or AD is the bisector of `angle BAC`
Hence the bisector of `angle BAC` passes through the centre .