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 Dec21 comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? @Hendrik Let's say he flips 2 coins at the same time, and they land on the floor. I can see only one of them, and it's a head. So, given that it's a head, the probability of the other coin showing a head is 1/3? Surely not. Now, in my visit to the family, I know nothing about their kids other than there are 2. Further let's assume that there is no reason to think that the first one I see will be a girl rather than a boy. But it is a girl. Given that that kid is a girl, the probability of the 2nd kid I see being a girl is 1/3? Dec21 comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? @Shai Let's say I visit a friend who flips a coin. The first flip is Heads. Are you saying that the probability of the second flip also being Heads is 1/3? Of course not. But then what is the difference between these two coin flips and the successive appearance of that family's two children? Dec21 comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? @Shai But why? Why is (b) different from (a) and (c)? Dec21 comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? I'm hoping that someone will show me why my 3 other examples are different from the case in question. a) the bowl of marbles b) my visit to this family c) my first child is a girl. The second? Dec21 comment In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? @Rawling Say I visit this family. I know they have 2 kids. One of them, a girl, comes into the room. The probability that the 2nd kid is also a girl is 1/2, no? Or let's say my wife and I have our first child, a girl. The probability that the next child we have will also be a girl is 1/2, no? Dec21 asked In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? Dec16 asked Sum of 1/n*n for n = 1 ,2 ,3, …? Nov30 comment Is Knopp's “Theory and Application of Infinite Series” out of date? Thanks. I thought that surely there would be developments in this area in the 60 years or more since publication that the modern reader should know about. None? Only a few? Actually, I hope there aren't, because I can see the book becoming one of my favorites. Nov30 asked Is Knopp's “Theory and Application of Infinite Series” out of date? Nov30 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? @Hans: Thanks for that. An extremely useful clarification for me. Nov29 awarded Supporter Nov29 awarded Commentator Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? @Hans: Ha! I see our comments crossed each other. I'll look at that other question. Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? But now I sort of do, because I just read the Wikipedia article en.wikipedia.org/wiki/Hyperbolic_function . Also Hans, thanks for the link to Inverse Symbolic Calculator. Very interesting. Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? Well, I have to confess that I don't even know what cosh(x) means. Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? Ah, you guys are amazing. Now, rather than asking for a proof (although I'm glad to see it), I wanted to know how you knew that my series could be taken apart into those 2 pieces, and that the limit is (e + 1/e)/2. Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? @Americo: There seems to be something wrong -- I see only what is to me strange code. Nov29 comment What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? @Hans: Tell me a bit more? Why is it that? Thanks. Nov29 asked What is limit of $\sum \limits_{n=0}^{\infty}\frac{1}{(2n)!}$? Nov20 asked Let $(n, m)$, $n < m$ be an Amicable Pair. Looking for large sets of integers that cannot be $n$.