Back to "The Burg"
Steve Landsburg brings us this little post-Channukah present : I think he mangles the logic and presents a totally bogus answer.* Let's read it: •Here’s the wrong answer: Every birth has a 50% chance of producing a girl. This remains the case no matter what stopping rule the parents are using. Therefore the expected number of girls is equal to the expected number of boys. So in expectation, half of all children are girls. {OK, Compare paragraph below} •Pretty convincing, eh? So why is it wrong? Well, actually, most of it is right. Every birth has a 50% chance of producing a girl — check. This remains the case no matter what stopping rule the parents are using — check. Therefore the expected number of girls is equal to the expected number of boys — check! But it does not follow that in expectation, half of all children are girls! { Yes, Steve, it does!! } •To see why not, let me tell you about the families who live on my block. There are 3 families with four girls each (and no boys)...