Question: 2014 Fall Final - 19

Author: Michiel Smid

When a couple has a child, this child is a boy with probability 1/2 and a girl with probability 1/2, independent of the gender of previous children. A couple stops having children as soon as they have a child that has the same gender as their first child. Define the events

A = "the second child is a boy"

and

B = "the couple has at least three children and the third child is a boy".

Which of the following is true?

(a)

None of the above.

(b)

The events $A$ and $B$ are not independent.

(c)

The events $A$ and $B$ are independent.