The Two-Child Paradox: Dichotomy and Ambiguity

Abstract

Given that one of the children in a two-child fam- ily is a boy, what are the chances that the other is also a boy. The intuitive answer is 50 : 50. More careful investigation leads us to a 1-in-3 chance. We investigate circumstances under which these answers are correct. The imposition of further conditions yields some very surprising results.