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1 . 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)
The events $A$ and $B$ are independent.
(b)
The events $A$ and $B$ are not independent.
(c)
None of the above.