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It is not possible to give a proper answer to the question because the children's are not independent. Among other things they depend on the parents' genetics and their age and there is no information on either of those factors. Also, the probability of a male child is not 0.5 as it is often naively assumed to be. It is, in fat, around 0.52.

However, if you suspend reality and assume that

  • the children's genders are independent and
  • the probability of a boy is 1/2

then the answer is (1/2)3 = 1/8.

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Q: What is the probability of a mother's first three kids being boys?
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