But if he tells you that his eldest child is a daughter,
Please use the more correct form of the problem which goes as follows: Mathematician: I have two children You: Is at least one of them a daughter? Mathematician: Yes.
If he just offers the information “I have at least one daughter” the probability distributions all depends on WHY he offered that piece of information, and it may depend on all sort of weird criteria. The form I stated above removes that ambiguity.
Please use the more correct form of the problem which goes as follows:
Mathematician: I have two children
You: Is at least one of them a daughter?
Mathematician: Yes.
If he just offers the information “I have at least one daughter” the probability distributions all depends on WHY he offered that piece of information, and it may depend on all sort of weird criteria. The form I stated above removes that ambiguity.