A household has two children and one of them is a boy. What is the probability both are boys? What if you learn instead that one of the children is called William?
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You phone a household and ask whether they have two children: yes. (1) You ask whether one of the children is a boy: yes. What is the probability both are boys? (2) Harder: instead you ask whether one of the children is called William: yes. Assume William is a boy's name and that both children could in principle be called William. What is the probability both are boys?
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