Family has two children and it is known that at least one is girl. What is Probability that both are girls given that at least one is girl?
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@Matti P. So what could be the answer 1/2 or 1/3 – maths student Jul 11 '19 at 10:49
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It depends how we found out that one child is a girl. The problem really is fundamentally ambiguous this way. You have to make additional assumptions to get a numeric answer, and the answer depends on which assumptions you make. – David K Jul 11 '19 at 11:22
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@DavidK can you elaborate which assumptions we need to make? – maths student Jul 11 '19 at 12:39
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Suppose you asked a truthful person who knows all about the family, "Is at least one of the children a girl?" Suppose they say yes, and suppose that's the only thing you've ever found out about the sexes of the children. Then the answer is $\frac13.$ But if that did not happen, but instead you met a girl and she said she is one of the two children of that family, you now know that at least one of the children is a girl, and the answer to the question is $\frac12.$ For further explanation, read the answers to "already has an answer" question. – David K Jul 11 '19 at 13:48