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ok, you stated this very well. It's now clear where the confusions arises: "Sampling this population ignoring any family that has no boys." Yes, with this inter
by iliketosleep 16y ago
ok, you stated this very well. It's now clear where the confusions arises: "Sampling this population ignoring any family that has no boys." Yes, with this interpretation the answer is 1/3, but it's contrary to my interpretation.
Actually, for anyone who is interested, see "Boy or Girl paradox". There is literature on this which discusses the different interpretations.
- tel 16y agoThat sampling arises because being part of the population which has no boys is * necessary and sufficient* to (truthfully) make the statement that forms the paradox. The alternative interpretation of the paradox arises when the wording of the paradox is construed to identify one of the children as male or female. In this case (stating something like "my first child is male"), being part of the population (x \in {BB, BG}) is necessary and sufficient and leads to the 1/2 probability of having two boys. In short, the question becomes whether you believe the child is identified in the wording of the question. Honestly, the author of the paradox goes pretty far out of their way to say "at least one of the children is male" avoiding that identification.