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Is my probabilistic for the problem of determining the probability, that a arbitrary chosen boy has a sister, if it is equal likely that a family has boys or girl and if the probability of having $0,1,\ldots,4$ children are $p_0,\ldots,p_4$ correct?

My idea was that $\Omega= \{n,\ b,g,\ bb,gg,bg,\ bbb,bbg,bgg,ggg,\ldots \}$ (where $n$ denotes the fact that the family has no children, $b$ stands for "boy" and $g$ for "girl") and $P(n)=p_0,P(bb,gg,bg,)=p_1$ and so on - and since boys and girls are equal like we get $P(bb)=P(gg)=P(bg)=\frac{p_1}{3}$ and so on.

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    Not much detail has been given. The sample space would probably work. Already some of the probabilities you have given are wrong. In a two-child family, under usual assumptions, the probability of two boys is $1/4$, as is the probability of two girls. The probability of mixed is $1/2$.2012-03-14

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